Native speakers tend to use comparative adjectives in preference to the "more + adjective," construction. So we would normally say "I feel much happier now," rather than "I feel more happy now." However, in this case, for a reason that I cannot explain, I tend to agree with Anthony that 'more proud,' sounds better.

These are interchangeable as far as I understand.

More proud is correct To me "prouder" sounds weird, I would say more proud.