At the moment, passport renewals are in the news for going through slower than a snail. As such, depending on when you will be travelling next, you may consider taking a risk and explaining the situation if asked than taking a punt on getting a new passport through in time. If you also have a driving license with your new appearance -- if you don't, its renewal should be cheaper and faster than a passport -- I would suggest that you carry it with you as well for some extra proof that you are you.