Trek FX 7.7 rear tire is rubbing the frame

Three steps: is it rubbing the entire rotation? If not true your wheel. Is it rubbing all the way round but just on one side, fix the dish of your wheel. If it is neither of the above, you need a smaller tyre.

All tyres will expand to a point as you increase the pressure. They will expand less and less as the pressure increases up until the point that they either explode or you destroy the rim.

There is also the question about why you are using more pressure?. Pressures much over 100psi are only faster as the road gets much smoother (dependant on weight of rider and tyre width), that's why they still use pressures towards 200psi on the track, but road pressures have been declining for years. It takes less energy for a tyre to deform than it does to push the entire bicycle up as it encounters a bump in the road.

Then it's not too much pressure.

That pic does seem to show the tyre over to one side slightly.

Perhaps dishing the wheel to the centre will fix it.

Update to the information I posted, new tires are 28mm (went to my receipt, sidewall hard to read), previous tires 25mm. [snip] One of the comments I received said that specs for my bike said that 25mm tires would fit

You're the victim of low tire clearance!

Good bicycles have ample tire clearance so you can run tires without fender, tires with fender, narrow tires, wide tires, slick tires, patterned tires, studded tires, etc. And no matter what configuration you use, there's ample clearance between the tire and the fork/frame/fender/brake so you can ride your bike anywhere, including mud.

Unfortunately, it appears your frame is only designed for at most 25mm slick tires, and even then riding on mud can deposit mud on the tire to scrape on the frame, fork and brakes. That's very typical of road bikes: they often have too little tire clearance.

There's no simple way of fixing this apart from changing your frame, your fork and your brakes (the brakes seem to be sidepulls with very low reach, so they won't fit on a frame or fork with ample tire clearance). I'd recommend V brakes or cantilever brakes, or better yet, disc brakes.

Because frame and fork swap is the most difficult replacement job in a bike, the best way to approach this is to sell the obsolete bike if someone really really wants to have a bike that can't take reasonable tires (most probably you won't find a long line of prospective buyers) and buy a new bike. When buying the new bike, avoid bikes that are labeled as "road" bikes and prefer bikes that are labeled as "cyclocross", "gravel" or "touring" bikes.