Unusual car problem on an old Buick?

[NightOwl]

I started having car problems a few weeks ago. The car was riding rough, and would get rougher the longer it was driven. Then it would stall when I came to a stop. I took it into a shop and was told it was the thermostat, the car was running hot and building pressure. Had the thermostat replace, it ran better for all of about 15 miles then started shaking again. Took it to another shop, was told theres a bad left inner tire rod (which explained a weird flat tire I had a week earlier) anyway, I was told the tie rod was causing the car to shake (being uneven or something) I had that replaced. I was limiting how often I drove because it just didn't seem like the problem was solved. Was told it needed a tune up, got that done, and a brake job. Drove the car today and for the first 10 minutes it was ok, then started running rough again, and the longer I drove it , the worse it felt. It didn't stall but felt like if I continued driving much longer, it would. What the heck is going on? I just put all this money into the car (with 3 different auto repair shops) and I still feel like something is wrong. Somewhere in the back of my mind, I recall someone else going thru this and it was either a fuel pump or a carburator. I know nothing about cars and have had coworkers advise me on the repairs before I had them done. I don't want to put anymore money into it unnecessarily. Its a 92 buick lesabre with 189090 miles (I've been told its a really solid car for the # of miles it has)