Call your local 211.
Just dial 211 on your phone and it will send you there.
Register as a homeless person, they will send you to a meet up place and see if they can give you shelter.
They are very nice to first time homeless people.
They can give you a pass to stay in the shelter for 2-3 days.
As for your gym, some homeless shelters have "shower time" they open the shelter to anyone and allow them to shower.
They also give you a mail box if you collect stamps or disability
fyi They dont allowed sex offenders there
Not sure about your area but in miami and broward we have soap kitchens that serve hot food daily
When you call 211 they will tell you where the soup kitchens are.
Next are food banks, usually some churches past out food once or twice a month.
Cereal, can foods, bread etc
Every other day a church is passing out food.
You cant keep going to the same one though.
Idk but when it gets cold in s fl we have something called emergency shelter.
When it gets below 50 they open for everyone to sleep.
Best bet is to meet up with homeless ppl and ask them how they survive.
Thank goodness you have a car.