You should consult an ophthalmologist who specializes in strabismus. If you live in the USA, you can use the directory at www.aao.org to find a board-certified specialist.
The use of orthoptics (vision therapy) to treat eye misalignment is very controversial in the USA, and you will get strong opinions on both sides. This type of treatment can cost thousands of dollars for sessions with a vision therapist, and it is usually not covered by health insurance. With 12 psd exophoria, you are at the lower end of the range of deviation which can be corrected with eye muscle surgery. I was close to your degree of deviation when I consulted a strabismus surgeon. (My condition had developed as an adult, so I had double vision as a result.) My surgeon gave me a home vision therapy program to take with me after my first visit. (You can google "computerized home vergence exercises" to get a link for obtaining the current version of this program.) I spent many very frustrating hours doing the exercises. (I failed some initial tasks more than 100 times before finally passing them.) By the time I had eye muscle surgery about 6 weeks later, I had reduced my deviation by a few psd's. The surgery was totally painless and eliminated my problem (with no effort on my part), so I never learned how much progress I could have made using vision therapy alone.
Your best bet is to become familiar with the aviation requirements and then consult a strabismus specialist.
I don't know whether the av