embarrassing for who? you or your relatives / friends? if your judged for not being married they're not good friends.
you dont HAVE to get married, also rather than having that conversation in front of relatives friends, talk to him.
give him time to open up and explore why he doesnt want to, maybe he doesnt want to explain in front of them, maybe with the baby he's just concerned about the costs, point is you will never know without asking. its not confronting him, just sit down and casually talk about the future, dont go off the rails try to get his viewpoint.
you previously spoke about being married with him so simply asking, "can you remember when we spoke about xyz (wedding venue, rings, how the wedding would look) we dont really talk about that anymore so i was wondering if you changed your mind at all?" asking it in an open ended non conflicting way without expectation.
at least then you can decide what your future together is like if there is indeed a future, depends how important marriage is for you.
people dont get married for many reasons.
going in with ;
Marry me or else
you said you'd marry me
why aren't we married yet
etc..
its going to push him away and isnt a healthy start to any marriage even if it did happen.