Hopefully your doctor will help sort things out. You might possibly need a higher dose of the levothyroxine (Synthroid), or another type of thyroid hormone. It would be good for you to arm yourself with knowledge ... thyroid disease tends to be long-term, and such an impact on many aspects of your life and health, not just fatigue and weight issues. The BEST website for thyroid information can be found at About.com. Here's the link to their Hyperthyroid information ..
http://thyroid.about.com/cs/hyperthyrdgraves/index.htm .. If you are now experiencing hypo symptoms (not uncommon, unfortunately, but very treatable with the replacement hormones), do check out the hypothyroid information while you're there (the link's on the left side of the page).
Being low thyroid can sap your energy, especially if you were hypER for a while before diagnosis -- you were probably going like a ball of fire then!! As well as lethargy, it's not uncommon to experience some mild depression; it gets better ..
.. Exercise will help ... but don't force more than you can handle, otherwise it defeats the purpose.
As for diet/nutrition ... controlling carbohydrates, and eliminating all sugars, refined flours and starches etc will go a long way to helping you feel better, not just losing weight. Keeping blood sugar and insulin levels stable by eating a diet higher in protein, vegetables and healthy fats will avoid the up and down swings that leave you feeling so bagged out.
You really do need to read at least one, preferably more - of the popular lowcarb program books that are out there. It's more than just a two-week menu plan of eat this, lose weight then go back to what you did before. To get you started, click on "Low Carb Tips" on the menu bar at the top of the page. Read the articles there, they're chock full of information about low-carbing. Especially read :
Low Carb Basics, Low Carb Frequently Asked Questions (FAQ) and
Jazz-up your Induction! ... You'll find lots of information to get you started, menu ideas and links to official websites of some of the popular programs.
Take care, hope you're feeling better soon. And happy READING
!! Keep us posted how you're doing.
Doreen