Let's not be hard on OP, she is taking in everything we say but it is hard to hear especially when you are in this situation.
I have come out of a 5 month thing just like this so had to comment. I was kept at arms length, not introduced to friends or family, cancelled on etc. However when I would bring things up I would be thrown scraps like 'My parents know about you' or 'I talk about you to my brother all the time.'
Long story short, he continued to keep me at arms length and sadly the truth of the matter was - he didn't want me as a girlfriend. By girlfriend I mean someone you introduce to family and friends. Someone you take out and publicly tell others you are seeing. Someone you mesh your life with.
I could still be with him now, I absolutely adored that man. But I know he would have never given me what I wanted because he was not ready to/didn't want to. :(
I'm not going to be harsh as I think you have had your fair share of comments here about that. What I would say is, that you have made yourself aware of the reality of the situation. The reality is - actions speak louder than words and his actions are not enough right now. Whether you communicate in person or via text, you need to explain to him that for you to continue seeing him you want to be INVOLVED in his life COMPLETELY. That includes being invited to his birthday - I mean, in all honesty that is a HUGE red flag that you weren't a part of that. You are a smart woman and you know this too.
It's hard to see when you really like someone. It's easy to lap up the words they say. Trust me, whenever I had doubts I would hear all the things I had been wanting to, just to keep me around.
Basically, changes need to happen or you have to walk. You are otherwise wasting your life with an emotionally unavailable guy, and you will continue to be a secret. Is that what you want? Clearly not, or you wouldn't be here.
You are not insecure, and you are totally right for feeling the way you do. Any woman or person would. So don't question if it's you being a bit OTT. You are in the right to want to be a part of his life after a year. I think you need to start thinking about what qualities you want from a relationship and then tell him that. If he can't give you what you want, you MUST be prepared to walk.
Big hugs xxx