Hi Queen,
I looked on several reputable sites, but there isn't any record of Vyvanse causing an increase in blood pressure. There are several other side effects, like the increased heart rate you mentioned, but nothing about blood pressure.
It could be anxiety, or your hyperthyroidism that is causing the blood pressure increase. Also, even though it's not listed as a side effect, sometimes when your heart rate increases that also causes an increase in blood pressure.
If your doctor thinks you might need medication for the blood pressure, there are several different types of blood pressure meds that I think you would be able to try. There aren't any listed side effects with other meds.
I've never been on Vyvanse, so I'm not speaking from experience, but it sounds as though it's working pretty well for you. I hope you're able to continue it safely.
Take care, slow