I just put new brake shoes on but hen I apply the brakes, it will pull to the right and then even back out by pulling slightly to the left. I'm not sure what is causing this.

 

You probably have a sticking driver side caliper. The car will pull to the left because it is always slightly dragging. When you hit the brakes, the right caliper works so it grabs more and pulls you that way.
Jack up the front and spin the wheels, you probably will notice more drag on the left one than on the right one.

 

You could also have a stuck caliper bracket pin that won't allow the brakes on the right side to fully engage. This happened to my wife's car not too long ago. When I took the brakes apart, the pads on the stuck side were only half as worn as the other side. A stuck caliper would also make that particular wheel really hot after driving a while. Oil or brake fluid on the brake linings can also cause this.

 

More likely, the rubber hose is all rusted up inside, and is blocked.

Change all 3 of em... all 3 are made of the same material, with the same size pinhole in them to begin with, have been on the same car, with the same moisture-filled fluid in em, for the same number of years, months, days, hours, & seconds; and are therefore most likely all in pretty much the same state. Renew ALL the brake fluid. MAKE SURE you don't let the master cyl run dry EVER while you're doing this, i.e. MAKE SURE you keep the reservoirs full of fluid.

 

That's it. As a long term owner of the same third-gen (24 years), whenever this happened, it turned out to be the rubber brake lines. Now I have braided steel lines and I change the brake fluid regularly so that it is never a problem.

However the stockers will last about seven years and then degrade inside the brake line. It's your lines.

 

It could also be a dead caliper, if new fluids and lines don't fix it.

 

+3 for the lines.

JamesC

 

make that +4 for the lines, had an issue where my car would pull hard right under moderate braking, changed calipers and pads, still did it.
changed rubber lines, problem gone