Yes very normal. I'm 23 weeks & still get sick everyday. My body doesn't seem to handle pregnancy well, as this is my third and I was sick all nine months with both of my previous pregnancies. As long as your eating something and drinking plenty you will be fine.
I also am exhausted day & night and want to sleep constantly.
I stopped feeling sick 2 days after I delivered my daughter and with my son it stopped @37wks!
Im currently 19wks and even the pills for nausea and vomit make me sick:/