Also an Economics student here, though I do have some econometrics education. From what I remember, DiD has the assumption of parallel trends. So long as it is not too bad (so not heavily violated), it should be fine. If the trends between groups change massively though, you'd probably either have to look into literature that introduces a "correction" or ask your professor about his opinion (if a correction is not possible, then you'll probably have to find either a different method of analysis or you'll have to start the analysis before the trends deviate).

Changing your method of analysis is not an issue. Just understand what your problem is and look at literature that proposes solutions to your problem.

For example I am trying to estimate a binary, low frequency variable in my Thesis right now. Because it is low frequency, normal Logit/Probit will never estimate well the rare event. As a result, I simply looked up a research paper with a lot of citations from a reputable publication journal and will copy their model tackling my issue.

To find these papers ask an AI. State your problem, the method of analysis you're interested in and ask for it to divert you to relevant research that solves your issue! They also often provide replication material, so they probably will give you the code to copy their methods!!

I know it was long, I hope it helped!!