Hi Bluebell
Like you I don't like taking medication (bio-identical HRT does not count as medication in my book!) but recognise that some conditions and some individuals, of course need certain medication!
Also like you I have very low blood pressure - sometimes in the morning it can be in the 90's/60 with slow heart beat. Notwithstanding your doctor prescribing this for you, that being the case (low blood pressure), in your position, personally I really would not want to take beta-blockers - - a heart medication designed to slow the heart and lower the blood pressure.
Palpitations and anxiety without an obvious cause (the former - heart problems. the latter - specific life events or stresses) are among the symptoms of menopause. May I ask if you take HRT? If not your oestrogen levels will now be low and in some women these symptoms you are experiencing seem to continue well beyond the cessation of periods. There are other ways of treating anxiety.
I don't know how old you are but depending on any other symptoms I would try to find another route than beta-blockers - maybe a low dose HRT if you haven't already tried it and are able to take it? This may help with the anxiety along with non-medication methods tried by many on here.
Sorry - not what you wanted to hear when you are looking for reassurance, but I am just saying what I would do in your position with similar blood pressure. I do experience dizziness sometimes on standing etc so would not want BP to be artificially lowered further.
I do hope you are able to decide to do what's best for you and then take those steps free from worry - and that you see an improvement as a consequence

Hurdity x