I don't know of any data regarding melatonin interacting w/ thyroid hormone but any pill has the potential to interfere w/ absorption of thyroid hormone. Might be worth trying to separate these by an hour or so.
You may be interested in this article,although the bulk of it addresses the action of a patented form of guggul on the thyroid... I'm not so sure that melatonin is a good thing for us hypos to take after reading this. Melatonin seems to suppress the action of the thyroid, which is why you're getting the same symptoms you had prior to taking levothyroxine.
Melatonin may help shrink goiter, or help those who are hyPERthyroid, but there really haven't been enough studies to recommend it.
Anyways, here ya go:
http://www.gugulipid.com/pre3.htm
Mzzchief