The fact that you described some of your stuff as "crap" means that you don't need all of it. Imagine that your apartment burned to the ground while you were out at a bar. What stuff would you replace, and what stuff would you not bother to buy again?
Keep the stuff your would re-purchase, and sell/give away the stuff you wouldn't replace. It sounds like you're moving far enough that you don't want to drive back & forth. Pack clothes you want to keep but don't want to wear in the next week or so into a box and ship them via UPS to your new new address. Clothes are fairly lightweight so it won't cost that much, and it will free up a lot of room in your car.
If you have items that are heavy, somewhat fragile and are due for replacement, this is a good time to do that. When my wife & I moved 900 miles, we got rid of our dish set, and ordered a new set on the Bed & Bath & Beyond website to be delivered to new address a day or two after our move in.
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