Anxiety in a relationship with two overthinkers?

My boyfriend and I started dating 10 days after we met, its been almost two months since we met. Every week has been some kinda rollercoaster where either im anxious due to my past but mostly keep it inside or his drama and secrets which he has slowly been revealing. He told me on our one month that he has a feeling we may not last long but still wanted to pursue it to prove his gut wrong. We both want a long term relationship.

We spent two days together when that happened and i was pretty emotional but he reassuranced me he isn't leaving and we still want to try and make this work. If anything since that incident he has become more communicative, calls me often and has started showing more of the loving, caring side of him. My friend kinda noticed a pattern that my boyfriend has these insecurities where he kinda pushes it on me which leads to a rollercoaster each week nearly and me being a similar person i can sympathize and be patient cause i have done the same in the past.

My boyfriend and I have a relatively healthy relationship that way where we respect each other and try to communicate whatever is bothering us. He is also sure to set boundaries with other girls who are tryna make a pass at him also so that i dont feel uncomfortable and out of respect for our relationship. The issue is he struggles to open up and sometimes has a shutdown where he is ok one day and then will be dry the next for sometime and he won't answer messages or sometimes even calls till he's better. I dont mind giving him space cause he is very used to being alone (he's been living alone since he was 14-15) but him doing this also fuels my overthinking and triggers my anxiety often because im in the constant fear of smth going down or being betrayed because of how my ex treated me and usually my gut feeling always signals something. Me have other health issues and anxiety problems get me confused if something is wrong or im just making a fuss for no reason.

Please advice!!

Updates
2 mo
by the way, were around 20. I would say it has been a rollercoaster cause we jumped into a relationship without enough time knowing each other but we also are clear on what we want. He is very loving otherwise and he has never disrespected me or been abusive in any form. If anything he has been amazingly supportive with my school and anxiety issues and I've done the same for him. We definetly share some values together too and dont give up on each other and loved ones easily.
Anxiety in a relationship with two overthinkers?
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