Minoxidil can be purchased in a pharmacy but is widely available online under the brand name Rogaine as a foam or liquid. There is also plenty of generic, cheaper minoxidil available. Some information about minoxidil can be found here
http://www.dermnetnz.org/treatments/minoxidil.html They're not entirely sure how it helps hairloss but it could be due to potassium ion channels. I'd be cautious if you have heart problems because minoxidil is used as a vasodilator but the topical stuff has such low absorption very little will enter your blood stream.
If you have traction alopecia then it might be irreversible so it's best to try to remove as much stress on the hair as possible. If the root of the hair is "tenting" then you are tying it far too tight. More information about alopecia areata can be found here
http://www.dermnetnz.org/hair-nails-swe ... reata.htmlI understand you want to make your beard look tight and tidy but try avoid using fixco, rubber bands etc. Also again it's probably not as bad as you think!
All the best