There are 2000 working hours in a year.
$13.50/hr is $27,000/year, before taxes. The poverty line is $33,000/year. Congrats! You're poor!
$20/hr is $40,000/year before taxes.
The average income across the whole nation is $50k before taxes.
You didn't say where in the US you are living which makes a big difference.
However even at $20/hr I think you're going to have a hard time affording rent or mortgage on a place with 3 bedrooms, plus food, clothing, utilities, insurance, cars, etc., all by yourself.