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I think that he should definitely have had some time to get over this other person before getting involved in a serious relationship with you.
You say you have been together for "little over two years" ~ this is a LONG time. Every single day is precious, and you deserve better than to feel like second fiddle to his past love.
I think that you should take a stand for himself, and tell him that he can only have one person in his heart at a time, and when he is prepared to move forward with YOUR relationship and not talk about his ex anymore, then you will be willing to be with him. This is depending on whether you have waited for him.
The fact that he doesn't want you to talk about how you feel about the situation is because it upsets him to talk about this other girl he is still probably in love with.