Tibialis posterior is the main muscle combined with the flexor hallicus that we spring off of. Regarding to the idea of fallen arches, unless someone has actually had a fasciotomy which is rarely done anymore, arches do not fall. If you have low arches, it is because you inherited them.
If you developed this problem while running barefoot, it is possible that there is more to the story to meet the eye. Typically, to fully understand this type of tendonosis, you need to look at someones gait, pelvis and fascial lines in the legs and throughout the body.
Short term, working out the calves by hand may be quite helpful, especially in the tibialis posterior muscle. If the muscle is shortened and tightened, you will get toe and foot pain. Doing things to it and using orthotics can be of some benefit, but relying solely on this is a losers game.
Find a good sports chiropractor who works with runners and knows myofascial release methods such as ART. I am guessing that your hips are torqued and that you have problems doing a level squat. Typically a tight tib fib will inhibit the gluts resulting in the lateral fascia of the leg tightening which is likely really the reason for your pain.
If you want to learn and understand your own body mechanics better, it may be a good idea to read my book Cheating Mother Nature, what you need to know to beat chronic pain. It is available through Amazon and can help.
Hope that helps.
Dr. C