Hey there. Welcome to AG!
Firstly, in order for us to help, we need to see what kind of swirls you're working with here.
Secondly, get a PC. I was like you when I was a n00b, I wanted to avoid getting a PC because I thought that I didn't know what to do with it etc. Buying the PC will be the best investment you'll make!
As for the swirls, you can remove by hand, but not all of them, just the light ones. You might like to try Meguiars ScratchX. That was made for defect removal by hand.
Washing and drying techniques play a big roll in maintaining a good finish. You will get light swirls even by using good tools and techniques, but then the swirls will be easier to remove! Have a browse on the AG store, especially at the PC kits.
If you have any questions about what you should buy, how to wash or dry or whatever, just ask and I'll be more then happy to help.
6LS2.