I don't know the OP's level of proficiency in or exposure to the English language and its usage. In general, looking up a word's etymology helps in its correct or preferred usage.
As Kate Bunting already note in an earlier answer, dissipate refers to thinning out by spreading in all directions (radially outward), while subside refers to lessening to a lower level (vertically downward). However, it's not always that distinct in usage.
subside: "to sink to the bottom," from sub "under, beneath" … + sidere "to settle," from PIE root *sed- (1) "to sit."
dissipate: early 15c., dissipaten, "scatter or drive off in all directions," from Latin dissipatus, past participle of dissipare "to spread abroad, scatter, disperse; squander, disintegrate," from dis- "apart" (see dis-) + supare "to throw, scatter," which is apparently from a PIE **supi*- "to throw, sling, cast" …
Pain can subside -- become less severe by going to a lower level, or dissipate -- become less severe as if by thinning out. Either way, it just means that the pain has eased a bit.
According to the labour ministry’s labour inspection office, average levels of dust are expected to be higher than the 50 μg/m3 limit on Sunday, but are expected to subside by the end of the day. (Cyprus Mail)
After battering Taiwan, the storm had moved inland where it was expected to dissipate, but Nina turned north instead, reaching the Huai River basin … (Ozy)