Are you subject to the home residence requirement on your J-1? You need to resolve that first if you are.

You can't just get a F-1 and then look for a school. You need to have be accepted at a SEVP-approved school before you can even apply for the visa. It is possible to do this in the US, but it still likely needs to be filed through the US Embassy/Consulate in your home country.

Most approved schools can offer you assistance in this.