1994 Ford Escort 1994 Ford Escort back tire vibrates

The right rear tire on my 1994 Ford Escort has recently started making a heavy thumping sound when accelerating and maintaining a steady speed. My brake light recently came on, but has been going on and off at a pretty consistent rate, so I'm not sure whether the problem is related. It occasionally seems like the car is bouncing in the back, and the speed of the vehicle is irrelevent to the noise. It does it all the time.

I figured it might be due to ice around the wheel wells, so I used a space heater to clear out the excessive snow buildup in my garage-didn't help.

I also noticed today that my car seemed to be riding lower on the rear right side than the left side. Upon closer inspection and rearranging my trunk, it seems this was not the case, but it still worries me. Could this be related?

I really just need to know where to start / if this is something I can fix myself or need to call my mechanic for.