Someone else would have to answer if the thyroid itself can cause dizziness or not, but I know when I was on synthroid last (and will be again shortly) it could make me dizzy sometimes. And take a look at your drug sheet that the pharmacist gives you? It may say that dizziness could be a sign of an allergic reaction. Mine did. I had hashi's and the synthroid would throw me hyper, so I'm not sure if it was the thyroid or the medicine. I start back on synthroid tomorrow. So I'm a bit nervous having had troubles on it before, but I have no thyroid now, so I'm hoping it will be a different situation.
thyroid dysfunction seems to cause dizziness in me
I am newly hypo after RAI and need frequent blood tests. Last month I had several days of dizzy spells and needed to lay down before I fell down. My BP ranged from 96/56 to 104/62. TSH had gone from 0.018 to 8.2 in one month.
For me, thyroid has a big impact on my BP. 6 months ago it was 196/135 when hyper.
So I would say yes, undermedicated can cause dizziness.