I (m26) feel like my girlfriend (f29) is insecure and its ruining the relationship

An incident happened yesterday which caused a lot of grief and I dont know what to do. Ive been with her for nearly 2 years and i felt that she was insecure because she had been cheated on before. Arguments happened here and there because of it but I do understand why she'd be insecure so I try to reassure as much as I can and be sympathetic. Im not perfect either and i have my own insecurities so i definitely understand what its like. issue is she doesnt listen to any reassurance and whatever I say she'd call it an excuse or try to twist it into something else. Ive been accused of being a cheater several times when i havent done anything like that and ive never cheated in my life.

So yesterday we were at the gym doing separate workouts. A woman came up to me and was saying that we went to the same university. In this moment im stressing out because this i knew this was going to cause grief with my gf. I just tried to have a closed conversation not inviting any further talk. I didnt know whether i should smile or not because i smile at everyone i see but if my gf saw me she would use it agaisnt me so I felt like very stressed being conscious of how I should talk and act. She was basically asking me general questions and I wasn't asking anything back so she went away after around 30 seconds. I texted my gf about what happened and she asked me to tell her exactly what the convo was. I was going through it and I could tell she was starting to become insecure so I asked her to not be. She then said along the lines of "oh but you couldn't tell her you had a gf" so I became firm and told her im not going to talk about it if shes going to be like that. The reason I was firm is because im genuinly tired of living life in anxiety and stress that anything can set her off. I thought maybe if I became stricter it might work but it didnt. She got angry and was accusing me of flirting because im trying to hide what the full convo was about even though I told her im not going to play ball if shes going to be argumentative and going into her habits. I get she'd be mad that I didn't say I have a gf but I felt like it would be weird if I just blurted out that I have a gf randomly. If she was like asking for contacts or asking to workout with me then yes but she was just asking what course I did and if I live around there. I was more than happy to tell her verbatim what the convo was but I just didnt want to be walked all over all the time so I held firm. I also asked her to come over to me so maybe that woman can see that I have a gf but she didnt. I didnt go to her because I was on cables which get taken a lot.

We got home and she locks herself in the shower and then she send me a picture of a woman I follow and says im following someone new. I told her that person is not new and it says on Instagram that I've followed her since 2019. So previously in another argument, she went though my Instagram likes and saw that I liked a bikini picture of someone and bought it up to me. Now I genuinly get why thats wrong so I apologised and said I won't do it and I haven't done it. I know it sounds dumb but I didnt like the photo because I was lusting, I just turn my brain off on Instagram and like everyones photos because they like mine. But she didnt accept any of that and just branded me a cheater and we never moved on from it because she would bring it up in future arguments. Anyways when that happened she said she took a picture of all the women i follow to see if i suddenly unfollow anyone in case I want to hide anything. And shes saying this new woman that she sent me wasnt part of those images. But im telling her Instagram itself says I've followed her since 2019 and you can even sort my followings by most recent and shes nowhere near the top but like always she doesnt listen at all and just calls me stuff like disgsting, trash, cheater etc.

And while this is happening shes running a hot shower for 1 hour and im asking her to stop wasting money like that but she didnt. I also had plans to go to the cinema with a friend so she prevented me from being able to shower and fix myself up. She then said that its funny how a colleague from work is following me on tiktok now but that account isnt that colleague they just share the same name. I know this because the person in the picture is a whole different ethnicity but its like she didnt even bother checking.

Then she just goes on a rant about the gym incident saying that I was flirting and laughing with her when I didnt and I dont know she can come to that conclusion when she wasn't there to see the convo. Then she says im just like her ex that cheated and that im somehow worse because I've portrayed myself to be a nice guy but im actually slimy. She also said im using all the same tricks he did and that she can see through everything. After about 30+ messages of generally the same ranting she then says trust me I made my ex suffer towards the end as well and asked why do I think hes still chasing her after this time which sounds very ominous (her ex is a weirdo and was harassing and stalking her).

She then said shes done with me but because I dont want things to end so bad she'll stay but she will play pretend in public (we work together). She said doesnt care about anything and told me to go to that girl and do whatever I want. She's saying shes going to act like a stranger at home and that shes not going to the gym anymore with me and not going to interact with me. Today she went to the gym alone and then came back and then I went. We share a car so I cant go if shes using it. She also took the sd card for the dashcam out I presume to look for evidence of cheating.

Im just lost on what to do. Ive tried to tell her so many times that shes insecure and that shes ruining the relationship. Ive asked if we could go to therapy so maybe a third party could assess things. I also made a point that a third party would be useful because shes accussed me manipulating things to make her seem crazy so i told her lets get a third party to assess but shes declining to. Its really frustrating because we do have a good relationship otherwise and im wiling to look past the other incidents of insecurity but this incident was way too much. We live together and have a lot of future plans and I dont want to throw that away but if she doesnt accept that shes insecure then I dont know what im meant to do.

Tldr: I feel like my girlfriend is insecure. A woman from my university came up to me at the gym and I just gave close ended conversation and shes exploded and said that im a cheater and then brought up many other things from before.