The general rule of thumb for Yom Kippur is that one may only eat if there is risk to life and not just for discomfort, even if it is extreme. So chest and stomach pains alone would generally not justify eating on Yom Kippur. However hypertension is a potentially dangerous condition, and one should consult their physician regarding the potential risk of not eating for one day.
However here there is an additional, mitigating factor that we are not discussing eating per se, rather swallowing pills which are not considered equivalent to eating food for the Halachos of Yom Kippur, and therefore there is room to be lenient. There remains the issue of washing down the pills which should not be done with water, but with a diluted solution of lemon juice or vinegar etc which would not be considered edible under normal circumstances.