They certainly can do. Depends on exactly what type of BP med your placed on. Beta Blockers can cause fatigue and weakness as an example.
You might be best served by using a diuretic in the first instance to see if this can control your BP. Also watch your sodium intake and try to eliminate it from your diet.
Your best bet first is a natty diuretic. Plus drinking more water of course. But sodium isn't necessarily the only culprit. The balance of sodium AND potassium is usually more to blame than just excess sodium per se.
Are you going to self prescribe these or are you seeing a MD? If self prescribing your crazy IMO. It just isnt safe. You never know what to expect. If your seeing a MD tell him you work out alot and dont want anything that will interfere with your workouts.