A bad tire still sounds like a good bet. Even though I have never had one quit the thumping by reducing speed to constant. Cold set was famous on older nylon cord tires at one time. But there are a lot of effects I have never or ever will experience. Sounds like your first car so try to enjoy it. It has been a long time since my first car but I think I still remember the sense of mobility and freedom it produced. Almost a high come to think of it. Certain things like gas at five gallons for a dollar and basic insurance for a hundred a year are not forgotten. Plus a carful of friends with some even in the trunk to avoid paying admission at the drive in. Wonder where all those girls landed up? if possible post the area you live in at the top. Helps to determine if you have a problem more notorious say in the rust belt or hot south sometimes. Some symptoms are climatic in origin as well. Perhaps you might make a local aquaintance with a simular car though the site. One is never too young to cultivate lifetime friends.