Yes, hypothyroidisn will cause eye twitches which will be so harmful to eyes because of the bad immune system and bacterium. As we know, the eye twitches will be easily caused by the bad habits of using eyes, coming invisible bacterium and so on. You need to use the eye drops to release the symptom. You should have the good rest for the eyes, not using eyes too much time in front of the computers with no rest.
It looks like you have got some serious trouble, sorry to hear that anyway. So, from what I know, hypothyroidism would give rise to an awful lot of symptoms to your body, but not all of them are critical. And twitching eyes could be possible, because the syndrome is so complex. But what matters most is your heart and your organs, so you should take good care of your health and follow the doctor's instructions.