I have a problem with noise from my heart pump somehow bleeding into my guitar amp. Has any other musician experienced the same or similar, and found a solution?
This type of thing is very common with electric guitars - they are designed to pick up string vibration in magnetic coils, and magnetic coils are also very good at picking up radio waves, and electrical interference from fluorescent lights, bad house wiring, and pretty much anything that can interfere with a magnetic field - like your pump.
The main solution is to use a Humbucker pickup. This uses 2 magnetic pickups with opposite polarity, so that the input from string vibration is increased, but input from interference is cancelled out.
You can also look at shielding the back of your pickup holes in the guitar, so interference is less likely to pass to the pickup.
Additionally check for good grounding - poor grounding does make interference much worse (symptoms include much greater interference when you don't touch the strings)
It's quite difficult to shield against a signal that happens to have a component at frequency one doesn't receive. I saw a case where a vacuum pump happened to vibrate at 25cps and molecular beam detector was set to detect only 25cps or multiples thereof. We had to shut off the pump during measurements. This probably isn't an option for your case.
Better filtering may help but there is often a resonance effect between the sender and receiver. The suggested alternate polarity pickups is probably the best method. One pickup receives the pump signal and the other sees the inverse of that signal and subtracts it. Both see the vibrating string as a real signal. Then the only remaining problem is a mechanical coupling of the pump through your hands holding the guitar; I would guess (never having measured this) that the signal would be attenuated your precious bodily fluids (blood) otherwise a normal heartbeat would show in the guitar pickup.