1995 Cadillac Deville Brake light and rear turn signals

I have a brake light problem with my DeVille. When I brake, the brake light on the left tail lamp works fine, but on the right side it only lights up in the middle and not the top part of the taillight, I changed the 2 bulbs on each taillight and its still the same problem. When I use the turn signals, the Left one starts blinkin slowly and then starts to blink fast, with the right one it just blinks fast. I am not sure what the problem is? Would I have to take it into the shop or am I able to fix it my self? The shop told me I have to pay 85$ so they can just see what the problem is. Any ideas on what I can do?