"T3 is o.k". doesn't necessarily mean it is optimal and it has to be. Exercise reduces T3 but it is recommended to do gentle exercises until you get to an optimum of hormones.
You must always get a print-out of your results with the ranges. Ranges are important as labs differ and it makes it easier to comment.
I feel sorry for you having your gland removed altogether and I think it would be a kindness to add some T3 to your T4. If you are in the UK, they have decided not provide T3 anymore so you might have to buy your own as many others have done on this forum.
Blood tests have to be at the very earliest possible. Fasting (you can drink water) you probably know this. You also have to allow a 24 hour gap between last dose of levo and test and take afterwards.
We need to know in particular Free T4 and Free T3 but labs rarely do these. Your GP should test B12, Vit d, iron, ferritin and folate. Deficiences can also cause symptoms. We have recommended labs who can do tests your doctor wont do, or labs even if GP requests.
Ask surgery for a print-out of your latest results, with the ranges. They may charge a nominal sum and post on a new question for comments.