Hmm those home BP checkers are notoriously unreliable as they need constant recalibration.
I too have low BP but when I become anxious it rises but have to say 134/84 is not very high. I don't take medication but do have to be careful when getting out of bed or standing up too quickly.
I have also had a tilt test but they had to abandon it as I started to panic
If you are coping in yourself then you don't need to take medication if you decide not to... but you may need to speak to your GP about this or ask for a referral to a specialist as you may be in danger of passing out if not controlled properly which has all sorts of implications in itself.
I think it is meno related as my BP has always been on the low side of normal and has dropped a little through meno - I try to eat little and often now as this seems to help me a lot and I do get some odd symptoms sometimes like shelves seem to move in shops or a muzzy head feeling but I just try to sit down and do some deep breathing.
Try to get more specialised advice before you decide.
Good luck
Smudgesmum xx