This actually could be a very, very simple fix. Take your car in to a mechanic or tire shop and ask them to check your spin balance. When you have your tires balanced, they place small weights on the wheels in order to prevent wheel wobble, if you've lost one or more of these weights, it could cause vibrations at high speeds.

I think you're expecting a little too much from a bunch of guys that don't have the benefit of a test drive in your car. That said, you can't run 44 psi, that's simply the tire's maximum. Sounds like you need to get the tires rebalanced and suspension checked, along with the wheel bearings.

Even though the tires are new it could possibly be a broken belt in one of your tires. Have you hit any potholes ? The way to check for a broke belt in a tire is to run your fingers around the sidewall of the tire. If you feel a lump or a spot that dips in then you more than likely have a broken belt in that tire. I drove a ford f 150 truck that would start shaking until you got up to a bout 55 mph then it would even out. I finally checked the tires and had a broke belt in my left front drivers side. If it is your steering wheel shaking then it could be a number of things like was mentioned before. The simplest thing to check for though would be a broken belt. If it's not tthat then take it to a tire shop and tell them the symptoms

Any vibration or shaking when driving comes from wheels. Out of balance, tire out of round, rim bent or out of round, rim not centered right on hub, faster you go, the more it will be.

Have you tried turning it off and turning it back on?

I asked this previously, however, no one really helped too much and I got a lot of answers that conflicted with other answers. I've done some experiments since then. My car was shaking really bad when I was going 70+ on the interstate, but it started after about 6 miles. I'm only on the interstate for like less than 10 miles so it isn't a biggie. I drove with tires at 44 psi (what the tires said) and 32 psi (what my car said), heater on (not the engine overheating) a/c on and no heat or air, top up with windows up and top down, cruise on and off, and I've drove on windy and not windy days! I have NO idea what to try next! The past two times I've gone to work or school on the interstate my car has not shaken so violently, but a little shake, until I let off the gas, then it shakes more until i get down to 40ish!

Sorry for the entire history of my life, I just want to give the most into possible for you since you're giving me your time!

I drive a 2001 Toyota Solara Convertible.

Thanks!