You don't say what your pulse rate is usually. -I mean at (say) 11a.m.? So it's difficult to know what to compare 130 bpm with?
It's perfectly in order for it to rise considerably first thing in the morning, because that's when you (well, -everyone) get(s) an automatic 'shot' of adrenalin upon instruction from the brain - to put the body in "Start The Day" mode. If you didn't get that there'd be something wrong, and you'd not be normal. It's because your body is in deep sleep, relaxed or "resting" mode. with minimum blood flow and needs 'booting' for it to cope with your getting up.
At the same time, as the adrenaline
kicks in, you'll notice your BP's also rise... it's normal too.
So, what's your "relaxed" pulse? -If it's 75 bpm 130 would be an unusually high rise. But if it's say, 95 100 bpm, then there's no need for concern
EDIT:- Marginal, isn't it? .... If it were me, I'd be cautious, and concerned , but not alarmed, and try to find the cause. - It's perhaps associated wit the medications you're taking?
My first question, -if I were your doctor, would be "has it changed? -When did the headaches
begin, and did the high pulse rate symptoms coincide in their onset?
Then -unless the medications are absolutely necessary, I'd discontinue them as a test, to see if there's a connection.