That and your doc can easily try a different BP pill. They work differently for different people.
I assume you are talking about your rest HR, i.e., the HR you get after you are settled and sitting still, otherwise if the 100+ is when standing and moving around, it may be fine.
Stop using all stimulants such as coffee, tea, cola, chocolate, anything with caffeine should be avoided. Decaf coffee should be ok. Then try to put your mind in a settled and relaxed state before measuring you HR.
And keep trying to talk it over with your doctor.