Welcome! The texture (curliness) of your beard is really nice and your mustache is indeed a fine one! You're absolutely right not to let the barber trim it anymore because that will only prolong the annoying period that it stays in your mouth. Yours does grow very straight and it's not particularly bushy or full, so you really need all the bulk you can get. In time, with that great contrasting color and fine hair texture, you'll be able to rock most any kind of mustache style.

Yes, wax should help. You can use it to train the hairs to lay back some. It's your call though. I think it looks fine as is, it's just whether it's annoying you.

Cheers!
Tom


Some helpful links:
Library Central of Beard Growing


Taming the Wild Mustache
Tips for eating and drinking with a big mustache

Excess on occasion is exhilarating. It prevents moderation from acquiring the deadening effect of a habit. ~ W. Somerset Maugham
A jerk with a beard is just a bearded jerk, but a bearded gentleman is awesomeness personified. ~ Triibeard