A.V.
You should consult your local lactation center for hand's on support. If you are talking about engorgement, yes you can still nurse but no, it shouldn't make you sick. Early on the body prepares to nurse more than you need and you can be engorged til it evens out. If you need to get your baby latched better, try expressing a little milk so your breast isn't so hard and then latching the baby.
kellymom.com is a good resource.