Could I breastfeed if I am sick?

Possible but depends. If you have a disease that you are supposed to be quarrantined, that's one thing, but a garden-variety cold, you're actually passing along some immunity in your breast milk.
Yes. If you are sick with a cold or other common illness, it is actually best to continue nursing you baby. Of course you should wash hands and try to not cough or sneeze on baby, wear a mask if you want to try to protect from a respiratory illness. But by continuing to feed baby your breast milk, you will pass the antibodies you are making for your own recovery to your baby, and can protect baby also.
Sure. You may breastfeed with most upper respiratory infections. In fact, we recommend it, as your baby will get type specific antibody to this illness, preventing her from getting it. Wash hands frequently, wear a mask. Hope you feel better soon!