I agree about getting your thyroid medication changed, if you need to, but not just for the sex. You will feel better, have more energy, have fewer sore muscles (if you do), and just be happier, in general. I also found that when I was hypothyroid, I had very little interest in sex. Now that I'm a bit hyperthyroid (for cancer suppression--not recommended for any other reason), I'm back to my old sexy self.
As for your husband helping out, maybe just asking for a few specific things, at first, would be better than just saying "I need more help." Men need specific directions, sometimes. After he's had a chance to unwind a bit after work, ask him if he could take out the trash for you, ask him to help you chop things for dinner, ask if he could get the towels out of the dryer for you, or if he could pick up dinner on his way home from work. Ask if he could take the kids to the park, miniature golfing, or something for a few hours on Saturday so you can have some time to yourself. Ask nicely and thank him for his help. It may seem like it should just be something he does without asking and that since it's for his benefit too, you shouldn't have to thank him, but don't get hung up on that. Once he sees that helping gets him more sex time, he might be more eager for chores.
If he complains about having to do things after he gets home after a hard day, acknowledge that. He has had a long day at work, right? And say (understandingly) that you have had a long, tiring day, too.
Just a few thoughts. Good luck with everything. If nothing else works, you could always take chocolate syrup and whipped cream and make your husband into a delicious sundae.