We have a sewer ejector in basement. We had a plumber put in a new one and then not long after had rotten egg smell coming from basement. I have been sick with vertigo (dizziness since Nov and have had all kinds of test and no answers. Can this be making me sick?

Sewer gas definitely can make you sick. Get checked out at an ER or your doctor, then call the plumber back for the correct fix. Doc first, plumber second