> I spoke with one PhD student about this and he told me most graduate student go
> through this and end up looking up answers online,
That's shooting yourself in the foot; I highly advise against it. If you need feedback, get it from your peers, adviser and other faculty at your school. Since they are in live conversation with you, they can solve your problems in a way that leverages your specific knowledge and fills your specific gaps.
> and that even some more post docs might struggle doing problems in textbooks (even > in their area of expertise).
Eeeeh... no. I mean, some might, but unless the problem in textbook is "prove the entire Poincare-Birkhoff-Witt theorem, no hints" (thanks Howe, I wasted four days on that), postdocs should be able to solve the vast majority of problems in textbooks and monographs of their expertise.
For your situation, the advise is quite standard: find a level of problems that you *can* do consistently and without help, and within that level start *slowly* increasing the difficulty and sophistication. This may involve some humility and time sink, as the problems you are able to do take you back to the undergraduate. Write complete solutions, read them back to yourself critically (possibly after a day or two has passed) and try to improve reasoning and exposition.
Find a faculty member that seems non-judgmental on this and ask them for assistance. It helps, despite what this sub often claims, to tackle some easier competition/putnam problems to push the limits of the more elementary machinery; just don't get too hung up on those.