You don't have homeowners insurance property taxes or PMI (private mortgage insurance) which, if you are getting an FHA loan, or have less than I believe 10% you will have to pay that in addition to your mortgage and this is generally not added into most mortgage calculators.
There is no way to make this work given the scenario. I'm sorry! If you even have the 3% needed to put down on a house...then you go on gov't assistance?
Let's just talk about the most obvious out of control expense--600.00 in gas. That's insane. ESPECIALLY given your income. 25% of your income is going to GAS to get to work? You really can't have it all. You can get to be with your boyfriend AND have a house AND stay in the school district.
Also, you're not going to get approved for a house at that price. Your housing expenses cannot exceed 30% (750.00) of your income and housing expense PLUS total debts cannot exceed 41% (984.00) of gross income. Not to mention as others have said, you wouldn't have $$ for house repairs, city assessments, savings...etc.
If you're just talking about rent, you're not going to make it based on the scenario you've described. You'll never get ahead, never have savings.
Here are some ways in which you can start to cut back: No cable, no internet. Nice to have, sometimes very important to have but based on the scenario, you can't afford it.
But the 600.00 gas expense is a non-starter. In other words, you can't get around the fact that you are asking the gov't (taxpayers) to subsidize your food for your family because you don't want to move closer to your boyfriends job and are literally pumping your entire food budget and then some into your gas tank (not to mention, gas is a variable expense).
Here's what you probably can afford:
No more than 720.00 in rent. This is the tippety top of your budget for rent. Ideally, I would say this should cover total housing expenses including utilities. Given your medical expenses, car payments, insurance, rent, cable, internet and cell phone that puts you around 1850, leaving you 550 for the rest of the month for food and other expenses. THIS IS DOABLE. Especially if you forgo the cable and internet. It's tight, very tight...but you can make this work and even tuck away a tiny amount for savings....
But the gas issue is a non starter. You literally eat up all your remaining budget in gas and then some...so even at your most conservative and realistic price point, you can't buy food, you can't buy clothes or makeup or anything..not to mention car repair, oil changes, or even WASHER fluid.
It's irresponsible to take money from the gov't just because you're unhappy at your parents house. There are MANY people who need it who don't have other options. YOU DO. You need to make some sacrifices. Give up the school district, sell your car, carpool to work with your boyfriend. So many ways to consolidate. You need to make sacrifices if you want to start living as an adult. Also, you didn't mention any child support. I don't know if the child's father is deceased or incarcerated but if not you should pursue that aggressively against future earnings even if he's unemployed.
I hope things work out for you in the future!