Can I get sick from a bed bug bite?

In general terms, no. That is, there's never been any evidence that bed bugs pass any sort of disease to humans when they feed on us. The biggest problem is taking care of the bites as you should with any sort of trauma to your body or skin. If there are a lot of bites and they get dirty you could have a problem. Or if you scratch them too much - that may also cause some problems. My advice is to seek medical advice from a qualified medical professional if you have any sort of bites just to be on the safe side.

One thing is for sure: you want to get rid of bed bugs if you have them.