You probably will pass germs to your child, not through milk but through conventional channels (sneeze, germs on hands, surfaces etc).
Your breastmilk will provide your baby with antibodies to said germs (assuming your body is fighting it off and you have no immune conditions).
Breastmillk will be the ideal food for your baby if they do get this cold, but hopefully the "priming" of their immune system from your antibodies will help them fight it off before it gets bad. But if they do get it, breastmilk is easy to digest and ideally suited to their needs. Feeding baby with a cold (and snuffly nose) is hard, they can't breathe and suck, so pull off etc. Try the saline spray for their nose, and the sucker thing to help clear out the gunk. Hve it on hand, it lasts for ages and useful when snuffles kick in at 3am.
Your supply may well of gone down if you're run down. Keep your fluids up, rest as much as you can and eat well. Feed baby as often as you can to build supply, if they are coming down with your cold, having extra time at the boob can be required anyway!
Remember breastfeeding is like a magic pudding, the more baby drinks, the more breasts make - so if you feel your supply is low, feeding baby more is the answer. If you used stored milk (or artificial milk) then production will go down even more, as breasts don't think baby needs the millk you did make.
It's horrible being sick as a mum with a baby, but try to do the absolute minimum, knock it on the head and then deal with the washing, shopping etc. when you're feeling better. Once you get tired it's hard to get your energy levels back.