Can motrin make my gout flare-ups worse?

Not usually. Ibuprofen is one of the ways to treat gout. We can have individual reactions to things. It's more likely that it didn't work and your gput flared anyway. Good luck finding something that works for you.
No. Anti-inflammatory medications such as Ibuprofen (motrin) are used to treat acute attacks of gout. These medicines do not make gout worse.