Welcome to BP!
Ten years ago I was in a similar situation you were in (though owed less) and paid off a chunk of my student loans right after graduating. Like you, I wondered if I had made the right move or if I could have started investing. People seemed uneasy about the economy at that point and there was a lot of talk of layoffs in my office. My loans were at 8% and I didn't know enough about investing to feel confident I could earn a higher return, so I made the decision to go all in and pay off my student loans as fast as I could. Also like you, I used a web calculator to find out how long it would take me if I added x amount of dollars to my monthly payments. That's what made me totally obsessed with the payoff.
I had two side hustles in college but since I got a job after graduating, I kept those side hustles and dumped the extra money into my loans. When I saw how much that helped, I started another side hustle and did the same. I also got a promotion at work. My payoff timeline accelerated quite a bit and when my loans dropped under 10k, it really fueled the fire under me. I had been driving a crappy car and eventually ditched that for public transportation. I didn't upgrade my cell phone, brought my lunches to work, said no (most of the time) to fancy coffee, turned down my friends a lot for hangouts (that one I kind of regret) and reduced my shopping down to almost nothing. I didn't have cable (or even a TV) and had no subscriptions to anything. I had been renting a room at the time of graduation for $500/mo, and moved into a different place where I rented a room for only $300/mo. That helped quite a bit. You're living at home, use that to your advantage for as long as you can.
Two years after graduating, I became debt free. I had nothing in the bank, but being free from debt was absolutely one of the best feelings in the world (so was seeing my friends again!)
I kept a couple of my side hustles going and continued to work hard at my job and earned another promotion. My savings rebounded rapidly, but real estate was appreciating like crazy (Seattle area) and I was priced out of the market. And you know what? At 25, I was able to buy my first property anyway, in a city that was fairly expensive (Redmond, WA) solely because of a partnership. There are always ways to get into REI that don't involve doing it on your own, keep that in mind!
If it makes you more comfortable to pay off your student loans and puts you in a better position to get into real estate later (debt to income ratio wise), go for it. You're already looking at part time jobs, maybe you'll end up finding a way to pay your loans off faster through those or through a promotion (or even moving to a different company entirely, which often means a raise). Have you looked into consolidating and refinancing your student loans? It's a great way to pay them off faster and you can refinance a few times if the rates are in your favor.
If you want to start investing in real estate, do it! I recommend talking with a mortgage broker to see what you can qualify for. It's free to talk with someone, and can really help you figure out where you're actually at, what you can eventually purchase and how to get there (including ways to improve your credit so you can get a better mortgage interest rate). There might even be first time home buyer programs with down payment grants or no down payment options in your area.
I also recommend not buying at the top of your budget unless the numbers make sense/you're ok with the risk/your job is stable. You could buy a house and rent out each room to cover your mortgage (also known as house hacking). This would allow you to continue paying down your student loans quickly, possibly even at the same rate.
Another way to start investing: does your employer offer a 401k with company match, and if so, have you signed up? Free money is always great.
Last bit of advice: while you're waiting for your savings to build back up, read as much as you can. There are a lot of recommendations on the forums for good investing books. Your local library might even have some of them as ebooks you can download and read for free. While I'm all for diving in and learning through action, it's good to be more prepared before doing so. You'll learn a lot of strategies and get a feel for what you'd be comfortable chasing after.
