I understand your anxiety for your problem.The tanning on back may not be because of bed along with intolerance to heat I would advice you to go in for
Thyroid function test.Also if you are putting on weight,test is all the more necessary.The test might indicate your problem.Hope you the test at the earliest and your problem can be tackled faster.In the meantime you can use Cream which has calendula on your back for reducing the tanning.Hope you feel better at the earliest. Thanks