Oh yeah, this is totally doable!
First, don't stress about the 403B. You don't need to "move" the money, just invest it from within the 403B. I agree with the investing advice above so I won't bother to repeat it. If you want more knowledge about investing, this should answer all your questions: jlcollinsnh.com/stock-series/ But for now, follow the simple advice above. You can have it done within 1/2 hour and get it off your mind.
It sounds like you were given a tough situation and you handled it the best you could. You were there for people who needed you, which is awesome. It totally sucks that you have to deal with the debt now, but you did the best you could with a difficult situation, so you should feel good about how you handled that.
You also got yourself into a situation where you're earning a lot more money, which is fantastic! You have a lot you can do here. As others suggested, getting a roommate or renting out art space could be a great way to bring in some money. Even an occasional airbnb rental would help, if you're in an area for that.
I question your utilities expense. That's awfully high. Does that include high winter heating costs that go down in the summer? See what you can do to lower that.
Definitely sell the car. You don't need it. What you need is peace of mind from the debt, and getting rid of that car loan will go a long way.
Instead of putting an extra $250 towards the student loans, consider putting it towards the credit card debt. Mathematically, it makes less sense, because the student loans have a higher interest rate. But you would only be doing this for a short time, a few months, and the sooner you pay off the credit card debt the better you'll feel. Look up the snowball method. I've seen it work for many people. The great emotional impact is worth a few extra months of interest.
You're making a lot of debt payments now. Obviously you could do more if you cut back on "extras" like your art and eating out, but you also need to have some fun. Instead, try finding separate ways to fund those activities. For example, I love to crochet, and I sell a lot of what I make. I use those funds to buy more supplies. I also donate a lot of what I make to a local homeless shelter. I can't afford to donate money right now, but the scarves and hats have even more value. Most of the yarn for donated items is given to me by friends who are happy to help out a good cause. What can you do along those lines? As someone else mentioned, you could donate art to a charity's silent auction, or maybe art lessons. You could give your art as gifts instead of buying gifts. You could sell your art and use that to fund more supplies. Get creative. (If you want to open an Etsy shop and you use my link, we'll both get 40 free listings:
http://etsy.me/1NV0saf )
You could also do some tutoring of kids on the side. In some areas you can charge a lot of money for that (a teacher friend of mine charges $60 per hour.)
While a lot of people take the extreme side of the MMM approach and try to cut out all unnecessary expenses, I don't think that works for everyone. If you have a hobby that brings a lot of joy to your life, don't give it up, just find another way to fund it.
Again, you're on the right track, so just try and be patient. You'll see a lot of progress over the next year as you pay off that credit card debt and apply those minimum payments to your school loans instead. And coming here is definitely a good move :)
