If I used my car to bring necessary supplies from home, does that count as business use?

Doesn't matter.  Employee job expenses are no longer deductible.

I am not an employee

If you work as a contractor and you are going to a place of business to perform your job, you are allowed to deduct the mileage to and from that place of work. If you have your own business and are driving to your office, then it wont be deducted as a mileage expense.