I have been on plavix since April 2009 after coronary stenting and it has never affected my bp wished it would. The only side effect I have had is that if I get cut I bleed easier and it takes longer to clot.
I have taken plavix twice in a 7 year period for 2 years total time. If you bump yourself you can bruise heavily, large areas. I banged my knee at work, it turned into a 7" oval bruise from my knee to my hip. A cut could cause you to bleed longer before you clot.
What other drugs are you taking? There are a number of drugs that cause your symptoms, most commonly beta blockers. I took Plavix for about five years, and it didn't reduce my blood pressure, but beta blockers certainly did. Until you find the answer, be careful getting up at night or after resting, sit on the edge of the bed for a bit before standing up.