Your doctor is right that, at the moment, you need to take it easy. Strenuous exercise uses up your T3, and I should imagine yours is low, at the moment. And, if you're taking levo only, you won't be able to replace it easily. Try just gentle walking, or swimming, until your levels are optimal - and optimal means when all your symptoms are gone. If what you do wipes you out for two or three days after, it's too much, and you should cut back. You have to get to know your own body, and how it reacts.
As for food, it's more a question of what you shouldn't be eating. And, the answer to that is simple :
* No unfermented soy or artificial sweeteners.
* No processed oils, like sunflower seed, or rapeseed.
* No processed foods because they contain all of the above!
Instead eat plenty of good protein, and good fat, fresh fruit and veg, some carbs, not too much fibre and don't skimp on the salt - adrenals need salt. And, don't count calories, count nutrients.
In fact, it would be a good idea to get your nutrients tested. Vit D, vit B12, folate and ferritin. These are often low in hypos, because they usually have low stomach acid, which makes digestion and absorption of nutrients difficult. And, they all need to be optimal for your body to be able to use thyroid hormone.
Hope that helps.