Clemsondoc I was diagnosed with high bp when I went in for a routine checkup. I had tried to sober up so as to "look nice" for the doc, but both she and the nurse gave me a look like they knew the story.
I fessed up, told them I was alcoholic. I still have troubles with alcohol but I do know it might take (my experience only) 6-9 days for things to settle on the bp heart rate front. Interestingly, and I researched this but could find nothing on it, heart rate and bp sort of see-saw during the first week. One goes up, the other goes down. Again, just my experience.
That said, unless you're convinced you won't slip, I have had no noticeable side effects from the bp med I take. Half the time it feels almost like a placebo, but placebos work surprisingly well.
Bottom line? Stay entirely sober starting now. Second, see a doctor. If he/she recommends bp meds give it a go. If you have side effects and don't like them, sign off. But I recommend taking your bp every day or two just to keep tabs on it.
Best wishes for your lifetime of sobriety! You can do it!