There could be a couple things going on. Did you say BP? Or were you referring to pulse. Pulse is different from BP. Both are VERY much related to thryoid meds.
Before your mom...gets too far with that Synthroid, I'd suggest her dose is a bit high to start with ( a slow increase is your best bet) and that she should be given some Armour too. Your poor mom...
The heart thing is usually a transitory issue for folks taking t-meds...and it will happen on whichever med the doc gives her. Every time there is an increase, this will happen. Its a an enzyme thing happening in the heart...and it can masquerade as hyper or a heart problem.
The doc should have been smart enough to outline this for her properly. Its a scarey thing for people. SHHESH!