My plan is to say my hands are shaking and the doc recommended some low dosage beta blockers and they will give me something...
You are too young to be this stupid. This kind of thinking usually only comes with age when the brain has started to deteriorate...
1. The pharmacist will NEVER give you anything that requires a script without a script.
2. The OTC stuff isn't as good as the stuff that requires a script.
3. Doctors who examine you will help you much better than wherever you got this beta blocker advice from.
They may be right, your doctor could prescribe beta blockers. They usually go with the simpler treatment first before they send you for all kinds of expensive and inconvenient tests if they don't have to.
Ask them how long to try it for before you go back if it doesn't work. Then the doctor will proceed to the next step.
Do NOT just go "meh, doc doesn't know, I'm never going back".
Go to the same doctor, they sometimes go by process of elimination, like it or not. Otherwise they would have to immediately do ALL the blood tests, cat scans and MRIs.
My dad had some issues which the doctor just diagnosed as a prostate issue. Got a blood test and some meds. When the issue became recurring, instead of going back, my dad just went for the blood test himself, and got some OTC meds. The blood test would show an infection, which would improve and then come back 6 months later. He would just self medicate with OTC.
If he had gone back to the doctor, he would have seen something was up and diagnosed the benign bladder tumor much earlier. As it was, he was lucky that the tumor was slow growing and that he didn't lose his bladder or part of it as it had already started to harden.
Again, what are you more likely to regret in 5 years time? Going to the doctor or not going to the doctor?