Please post your FT3, FT4 (and their reference ranges) and TSH results.
300 mcg (going to 350) is a pretty hefty dose. Are you a large person?
Since you are on total hormone replacement after a TT, there is really nothing that can be damaged.
I had a total thyroidectomy seven years ago and am having a lot of trouble keeping my TSH and T4 levels under control. I am currently on 300mg Eltroxin and now my specialist want to increase it (very reluctantly) to 350mg. I constantly have palpatations throughout the day and I suspect if my medication was increased it will only get worse. I do wonder with my blood tests being out of control for so long if they have created some long term damage. But asking my specialist questions like that get me no where.
Also, discuss this with your doctor and get your calcium checked. Make sure your calcium is not too high or too low.
It could be a symptom of hyper or hypo.
Your hormones are still getting settled, and you were either hyper or hypo or both after surgery and RAI. Your body is going to need time to heal.
You are still in the "get used to a dose of replacement hormone" stage, and it may take a while to find the right dose of the correct med to get you feeling well.
You should be getting tested often. Every 4-6 weeks for several months. A TSH, a Free T4. Untill your level is where you and the doctor wants it and it stays there.