Just because you're part time doesn't mean you have to be part time. Most schools will make you an employee and sort out tax for you, and probably pay you monthly. You could easily be an employee with several companies.
I would be careful about using club a/c and calling yourself self employed, therer was a thread about it earlier and the outcome I seem to remember was that it is a bit iffy and you should be carefull, or ideally know your facts very well.