The Play-Doh is a gel, and therefore cannot be carried on unless it is a medical supply -or- in a quantity smaller than 3.4 ounces and fits in your liquids baggie. Convincing a TSO that play-doh is allowed is questionable and you risk seizure of the item. It is completely legal in checked luggage, the only concern is that it will have characteristics similar to explosives and may trigger a bag inspection.

You can look around at the Halloween candy at your local grocery store. They usually have small tubs of play-doh (to give away instead of candy) that are smaller than 3.4 ounces. This would make it easier to carry-on if you are not checking luggage. The key is you need it in writing on the label that it is less than 3.4 ounces, so I'm guessing an egg of Silly Putty won't work.

It may sound absurd, but here is what I would do:

Pack it in your checked bags; put the original unopened container in a plastic quart or gallon baggie, with a copy of the therapist's instructions in the bag. Put it on top of everything else in the luggage, so when they open the luggage, it will be the first thing they see and they won't have to paw through your undergarments. Don't pack anything valuable in the bag, with the Play-Doh if you can reasonably avoid it. I wouldn't pack any electronics or cords in the suitcase with the Play-Doh, either, because that might make it look more bomb-y.

Personally, I would also seal the luggage shut with a zip tie, so I could verify whether or not anyone opened my bag; if so, I would check it for missing items before I left the airport.