Oh for fuck's sake.
Dude. This is not running away from your problems. This is SOLVING YOUR PROBLEMS. This is the literal definition of the perfect answer to everything you've been not dealing with. Your horribly messed-up sexless relationship, your passivity and acceptance of playing the role of martyr, your dead-end job that isn't using your skills or challenging your intelligence or offering you a single rung up the ladder for advancement let alone reasonable pay, a change of scene, a chance to move to someplace where you already have friends and support system there and willing to give you a place to live and help you out and be social with you... great zombie jesus, do you want them to bake you a plate of cookies and give you a back massage in addition before you wake up and see this is the kind of opportunity that most people would kill for? This is the fucking Deus ex machina divine intervention that silly/great movie plots hinge on - you're not possibly going to pass this up are you?
Running away from your problems is EXACTLY WHAT YOU HAVE BEEN DOING FOR THE LAST 7 YEARS. Despite the verb "running" indicating action, you've spent your entire relationship avoiding that giant Very Insanely Big Mess that is your romantic relationship. You've hidden from it, you've avoided it, you've bent yourself into stupid painful shapes pretending that everything is just fine, this is normal, stuff like this is totally okay and you are now numb and distanced from living a real, in living color and with all the amazing colors and sounds and feelings out there... because you've spent the time RUNNING AWAY FROM DEALING WITH IT.
Moving and taking this job is literally whatever higher power/deity/karma/clockwork that you may believe in handing you your golden ticket. This is your out. And it's "easy" like something easy is necessarily a bad thing? Who the fuck cares if it's easy - not that I think it is since we're talking uprooting your entire life and moving to someplace you never even considered before - but if you think this is easy, even better! You've been handed pretty-awful and stuffing down your wants/needs for years... you've earned "easy" at this point!
Do NOT let your girlfriend's pessimism and lack of support blind you to the fact that this is AMAZING opportunity. She is not considering you at all here (again). She is only concerned for her own self - she is selfish and self-centered and needs to grow up. I still don't think she's doing any of this intentionally, but until she gets her own head straight, she isn't fit to be in a relationship... and you are exactly the same. Sad thing is, you need to grow up too, and neither one of you are going to do any growing or maturing or working towards being really content/happy if you stay together. You need to leave. Hell, if you are that nervous, don't sell and just rent the house out, and promise yourself that if you hate San Antonio you can come back there in a year. But GO and commit to doing your damnest to having fun, growing up and work on you.
San Antonio is actually a pretty nifty place - GREAT food, fun stuff to do - amusement parks, sports, nature/state parks, RIVERWALK and FIESTA for the crazy party stuff, lovely people for the most part, museums, beautiful, old world buildings and lots of cool stuff a 20-something guy should be REALLY happy to experience. I personally think San Antonio is one of the best cities in Texas - I'm a transplant myself in one of the not so great cities - but I honestly can't see living anywhere else despite the slightly annoying "crazy Texan" personas you'll meet down here (they put the flag/lone star stuff on EVERYTHING. You'll be fine tho, promise). Heat sucks, but it's pretty nice in the winter months and just wear sunscreen/hats/drink lots of water and get in the shade or A/C if you start feeling too hot. Or go swimming. Or river tubing, or the many waterparks...
Just try it. Even if you hate it, give it one year. You get some space to find who you really are without being tied down to someone that was happy to cripple you emotionally/physically and get some great job and living experience and have the safety net of friends in the area.
Break up with your girlfriend, give her a few weeks to move out, then either put the house up for sale or rent it out. Do NOT contact your old girlfriend and make sure to block her on social media/phone. Do not call her/text/message her. Move to San Antonio and take that job. Date LOTS of different people. Do NOT start any new relationships other than casual stuff (no exclusive dating) for at least 6 months to a year. Get a counselor to work through the relationship stuff and your self worth and confidence.
You are worth more than what you are getting now - both in your career and in your relationship - please don't pass this opportunity up. Someone out there throwing you a lifeline while you're drowning. Just grab onto that rope and don't look back.