I appreciate the comments I’ve gotten. Cadillac people told me my back struts are a “little” worn but not bad. I had the tire rims checked at my regular Cooper tire company (they had to balance the Goodyears I got at Wal-Mart because they did a poor job). They said the rims were okay. By a process of elimination I may have an alignment, although there are no signs my car needs one.
I’m going to another garage this afternoon to have another inspection. I’m having doubts about the tires being the problem at this point and I don’t want to spend $400 plus for new tires if that’s not the problem.