As a descendent of Scots I'm not surprised your compressor is so stingy with air!
I think you need a new compressor if 3psi is all it can do. I'm guessing 30psi is it's capability and yes I think you need a regulator to get the most out of your airbrush. You can buy them online at places like Bear Air or Dixie Art, but you can also get them at hardware stores.