When I run the shower, mostly hot water, the pressure will run normal for a minute, then raise for a minute, then repeat. My home is supplied by a well. What is causing this?
You are experiencing a fairly normal event for a well with pump and pressure tank, though if the behavior seems new & different the pressure tank may require maintenance or repair/replacement.
Most well pumps (there are exceptions, such as "constant pressure pumps") run on a simple differential pressure switch with a 20 PSI differential (often non-adjustable) and a somewhat adjustable setting (20/40, 30/50, 40/60 are probably the most common settings.) When no water is being used, the system holds pressure due to a pressure tank; when water is used, the pump is activated when the pressure tank falls below the lower setpoint, and the pressure rises as the pump runs, until it shuts off at the higher setpoint - water has been added to the pressure tank, which again supplies water until the lower set point is reached.
If the air cell (most typical these days is a "bladder" or "diaphragm" type of tank where are and water are separated by a membrane) has inadequate pressure (possibly due to a leak) the amount of water stored in the pressure tank becomes smaller, and the pump operates more frequently - this is both more noticeable to you, and worse for the pump's life expectancy.
If you turn off your pump and drain the water from the tank, the air pressure should be roughly 2 PSI below the lower setpoint (18, 28 or 38 PSI for the typical setpoints listed above.) If you can pump it up to that value and have it stay, that may be all you need to do - if you find the pump operating more frequently in a short time (and drain the tank again and find the air pressure is lower again), or you can't pump it up at all, you may need a new pressure tank or a new bladder (I have personally found replaceable bladders to be non-ecoomical .vs. just replacing the tank - shop and see what you find.)
It is also possible that your tank is fine, but could be larger (or could be two, which is effectively larger.)
Or, you could convert to a constant pressure pump system - but those have always seemed excessively expensive to solve a "problem" that isn't really a problem with a properly designed and functioning pressure tank system - to me. That's an opinion and budget call.