first you have to be very specific that you are wearing partial denture in anterior or posterior region,
because this pain may be due to overextended denture as you are saying that they are ill fitting.
to rule out this stop wearing your denture for 1-2 days, if you start getting relief than this is the only cause & you have to go for realignment.
After extractions we always wait for few months before making denture because bone resorption
is very fast in first few months of extraction.
if you feel any gland enlargement, and don't get any relief than better visit your ENT surgeon & in the mean time you can start up with course of antibiotic including azithromycin
500mg once daily for 3 days & ibuprofen
400 mg (SOS) , don't do any heat application by yourself.