A homeless shelter won't take your child and they have a two week maximum stay. Then, you will be kicked out. You are WAY off in what you will need in savings to rent an apartment. Professionals recommend 18 months of rental payments. That's $12,600. You might be able to get away with $10k in savings but 3 - forget it, especially with a child. You just have no clue. You are not likely to qualify for housing assistance and even if you do, you won't get in right away. Waiting lists are about 3 years to 13 years, depending on the location. How is it that you have only $3,000 saved when you are living with your parents. What do you do with your money? Flush it down the toilet? I suggest you budget and work your *ss off and save more over the next year. Then consider moving.
Certified Paralegal, with 25+ years' experience & with Landlord & Tenant law experience.