It's always best to separate other drugs from your thyroid medication by a few hours, as some may inhibit absorption of the thyroid med; call your pharmacy for information on drug interactions.
Likewise, I was never told to avoid taking anything with my levothyroxine besides food and calcium/multivitamin (basically just not at the same time, but I could still have a multivitamin). I've also never had a problem taking benedryl (besides that it knocks me out) or any other drug with my hypothyroid meds.
If you're on a drug for your hypothyroidism, there is this nifty tool at the top- under drugs, you can find drug interaction. All you do is type in the drugs you're on (otc and other) and it will tell you what interactions are known with it. And if all else fails and you're unsure you can always call up your local pharmacy. They will be able to tell you if a specific drug will react to another.
I am going to assume you are on medication for your hypo? You can always call your pharmacy to make sure.
I have been on thyroid medication for over 17 yrs & take whatever OTC I need to take for whatever is alling me.
I was never told not to take anything OTC..