sounds to me like you still need the docs to have a quick look and check the BP is now firmly down...then you can go for it running-wise as much as you like. My understanding is that gym work is actually more dangerous than light running/swimming.. and make sure your docs continue to do those regular checks on renal function etc...
as said earlier in this forum, high BP is completely manageable and shouldn't hold back your running...and it's good news that it's been spotted!
they shouldn't give you a certificate if the BP is too high and not under control because this is potentially dangerous and you simply shouldn't run. in my case, the heart muscle had actually slightly enlarged because of the extra strain the undiagnosed high bP was putting on it. but as soon as the BP was controlled, the docs were happy to give the all clear, telling me the muscle would slowly revert to normal size. in terms of the medication, even once you're ok to run again they need to keep you under review, check kidney function etc. it's all sortable, but don't put yourself at risk for the sake of a month or two off running.
and the drugs don't seem to have made any difference to me...i'm running strong at the moment. so have patience and good luck!