Ouch, that doesn't sound fun at all!
It's hard to say what might be the cause without seeing you punch - having said that, you might be tensing your neck when you are in the class which would cause all the muscles to complain.
I'd recommend getting yourself down to a good remedial or sports massage therapist (or similar) and getting them to take a look. Chances are they can work knots out of the muscles (if it is muscular) and ease the pain.
To quickly reply to the lady below the OP with the headaches (sorry the reply window has covered up your profile pic and name!). If your getting headaches from super tight muscles in your neck and shoulders, I feel your pain. I get headaches that last for days and pain killers don't touch - they are usually fixed by a good massage (Swedish, Remedial, Shiatsu or Sports) as I find the headaches are from the muscular tension. I've ended up getting massages every month / 6 weeks or so as part of my 'prevention not cure' plan.
Hope you guys feel better soon!