I had a similar problem with my tj 2 year ago, was just a bad set of tires, nothing else,
Once in a blue moon this summer after hitting an uneven bump at highway speeds I would get a little death wobble, I replaced the steering stabilizer on the front axle, havnt had a problem since, rubing stock tires you should be good to go, wait and see how new tires run, it could always be warped disks when braking at highway speeds,
Before you pay a bunch of money to a shop, see how the tires change things, it's more than likely a minor issue you should r able to resolve yourself