High arches in the feet (the medical term is pes cavus) is a deformity of the foot in which the arch underneath is elevated and the front of the foot tends to tip down. There may be other associated deformities, such as "hammer toe" or "claw foot."
Although some cases of pes cavus are idiopathic (meaning not caused by an underlying medical disorder) many are in fact associated with diseases of the nerves and muscles. One of the most common diseases associated with pes cavus is, as you mention Charcot-Marie Tooth disease. The probability of this is raised by the fact that you are experiencing tightening of the muscles in your calves. The combination of pes cavus and a tight heel cord is called the pes cavovarus, and this the form of high arches most commonly associated with Charcot-Marie Tooth.
Asymptomatic cases of high arches do not necessarily need further workup. However, in your case you are having some symptoms, such as tight muscles. Therefore, I think it is worth while being evaluated by your doctor
to see if you need further workup. Start with your primary care doctor
, who then may decide to refer you to a neurologist
for further testing.