Underwriters will count at least 1-2% of your student loan balances as your "monthly payment" if you are on any income-based repayment plan, even if your payment is actually just $100/month. I don't know what your repayment plan is, but underwriters will count at least $2300/month as debt against your DTI. That is in addition to your other debts.
The best DTI you can probably hope to achieve with a bank loan is about 45%. This means your monthly debt payments can total no more than 45% of your monthly income. You're smart people and can do the math yourselves, if you haven't already spoken with a loan officer. I suspect that your DTI is already over 45%. @Frank Jiang was very generous with his time in coming up with a hypothetical scenario for you, but I'm guessing your debt payments are even worse, since he's assuming that your car and house payments are (roughly) based on the current balances rather than the original principal.
So unless you can get a private lender to lend you the cash at an interest rate below your lowest extant loan (i.e. car?) rate, and unless the property was guaranteed to cashflow at a cap rate that is at least 2-3% higher than your highest interest rate loans (school?) it would be imprudent and unwise to accumulate any more debt until you have paid down existing debt and/or lowered your expenses.
Were I in your situation, I'd:
0. Make sure you have an emergency fund of at least 3 months' worth of living expenses and good health/home/liability/disability/life/umbrella insurances.
1. Pay off the credit card and keep it paid off each month.
2. Concurrently with #1, I would see if I could get an equally reliable car with a lower monthly payment than the one with the 10k remaining on the loan, or ask myself whether I even needed a second car (maybe in Texas, you do, but it's also possible to carpool, take public transit, bike, etc.) And/or if the paid-off car is a nice/expensive one, I'd sell that and pay cash for a more modest used car. I lease a 2015 hybrid gas/electric plug-in (Ford C-Max) for $234/month. It's a $35k car, but federal tax credits for electric vehicles make the monthly lease payment low. But I digress.
3. Then I'd start paying down the Wells Fargo student loan, throwing anything extra towards the principal (you need to tell them that you want the extra payment applied to the principal, rather than pre-paying the loan). After that's paid, I'd do the same with the government student loan.
4. While I'm doing all/any of the above, I might also see if I can get cash-out refi with a very low rate to pay down the student loans (private first, then government) as much as possible. (Chances are slim though because to get a refi, you still need a good DTI. It's a chicken/egg scenario, but maybe a community bank would do it.)
5. I don't know what your house is like, but if you can get a lodger to rent out a room, or if you can add a separate space by inexpensively finishing a basement or attic (microwave, hot plate, mini-fridge, bathroom, + bedroom or studio), you can use that income to both pay down debt and to establish yourself as a landlord in the IRS's eyes.
6. If and only if the numbers work out for your current residence, you may consider renting that out to a tenant and then renting a much less expensive place in which to live (closer to work so you can get rid of one car and its related expenses?)
Essentially, pay down your bad debt (which is pretty much everything except maybe your mortgage) before you accumulate any more debt. (There are some rare exceptions to this relating to interest rates that I would probably only suggest an experienced investor make.)
Your first rental will cost you more (in time and money) than you anticipate.
I also second everyone who suggested house-hacking as a way to get your foot in the door of RE investing and re-evaluating current desires vis à vis life goals.
Lastly, this isn't advice and I'm no CPA/lawyer. It's just what I would do were I in your situation.