I've been smelling brake fuild for a while, and I don't drive that intense anymore, so I took it to a shop. They lifted it up, and the guy tried to spin the driver's side rear wheel. Definite a problem with that side of the brakes. The guy said it's probably the caliper is probably freezing every now and then. Estimated replacement is about $360 for both calipers, pads, labor, etc. I know that it's customary to replace both sides, but I'm probably gonna sell the car in a few months. So, I want to make this fix as cheap as possible, e.g. probably DIY.

Can I replace just one caliper? or Are there some other things I can do to rebuild it?

If just one caliper is bad, that's all you need. But b4 u replace it check the slide pins. if the pins/bolts are seized, the caliper will hangup. clean & lube or replace them if they're stuck.

25000 km ago I replaced both rear rotors, pads, and only one caliper ( pass side) . No problems whatsoever. Yes you definitely can replace only one side.