"Proud" in this case means not only "con orgullo" and "con arrogancia" but also quite a lot of "de forma imponente". And "do myself up" means the same as "dress up" and has the sense of "vestirse de etiqueta" and "poner elegante".
Right on Garry.
Truth be told, I've never seen this expression in more years than Garry has been around. To do oneself proud is fairly common. I would translate it
roughly as portarse de una forma que merece orgullo. But, to do onself up certainly appears to refer to how the person is dressed. So here's my guess, and please keep in mind it is only a guess:
Me vestiría muy bien... or, less formally, me pondría muy chulo.
Let's hope someone else chimes in who has a better notion of what is really intended here. In this case the difficulty is not translating; it's figuring out
what the author meant.
Saludos a los dos,