Stay at home for a few more months and see what you can save. How long have you been saving to get to 13k?

Over the next 3 months, save 2800 for rent. At least 150-200 for utilities. 50 for internet. 200-400 for food (do you cook/make every meal, or do you eat out). 250-500 for random expenses.

Sure, some of those numbers might seem like more than you need, but always have a plan for higher expenses.