"Tingly" feeling is often caused by vitamin B12 deficiency.
I sometimes get this actually. I get pins and needles and numbness all over my body. At times it does feel like something crawling. As subire mentioned I wonder if it is a type of tingly feeling. I live with this daily.
Are you having allergic reactions to scents, fabrics, even your detergent or shampoo or anything? Different people describe things differently, but I am wondering if what you are describing is what I describe as tingley and itchy, due to it most likely being a lesser version of yours.
There are many recipes for making home shampoos, scents, candles, detergent, etc. Most common is baking soda & soap shredded for detergent (I'd recommend castile), maybe a few drops of an essential oil you like and have no reaction to, and baking soda for hair (can also add essential oil). Try changing up your routine to stuff that shouldn't effect you and see if you notice a difference. If you switch up a few things and notice a lessening, you can work on finding more recipes for everything you'd need to do in your home, although you'd still probably have issues out in public, as those are out of your control, but with less (and less close) aggravation they should probably lessen.
I've never heard of skin crawling as a symptom of hypo. Levothyroxine is identical to the hormone your body would produce, if it could; therefore, I'm not sure how you could be allergic to it. Some people have reaction to the binders/fillers or dyes in the various pills and often find that if they simply change manufacturers, they eliminate the reaction, since all manufacturers use different fillers/binder or dyes.
There are several varieties of skin mites that could cause the crawling sensation. You might ask to get checked out by a dermatologist.