Keep a connection to your cardiologist, and I think it good to ask him about some relief from the high HR, maybe a low dose beta blocker. This will have some affect on the monitor reading, but I consider a resting HR of 120 too high to let it run for weeks without treatment.
Any affect of a low dose BB will be on the intensity of what the monitor is looking at, I think it unlikely that it will mask any arrhythmia. I could be wrong on this point, but if so, then have a beta block to start as soon as the monitor comes off.
Your family history also strongly suggests that you have a nuclear stress test, there is no problem doing these things in parallel.
Being 20 yo is something on your side, but heart failure can happen at any age,
I'm 20 years old. My resting heart rate is 120. When I run it spikes pretty quickly and has reached 195 before. I've had the EKG and it hasn't shown anything. I'm having a monitor put on in 2 weeks.
Thank god you are seeing an cardiologist. What test have been run? You condition is potentially serious, and must be fully diagnosed.
If your HR is 120 at rest that is "something wrong" what's with your cardiologist? Or is 120 the HR when running? There's a big difference as I"m sure you and your personal trainer knows.
Given you symptoms (don't know your age) I think you should undergo a nuclear stress test and an echocardiogram and a monitor if the EKG doesn't show any electrical/rhythm problems.