You cannot get tonsillitis, however you can get an infection that affects your throat and vocal cords. That includes strep throat.
Tonsillitis - not likely since no tonsils. Strep throat - much more likely since your throat doesn't need its tonsils to become infected.
Unlikely ( but not impossible) to get a bacterial infection in your throat without tonsils...but you can still catch viruses. You doctor should be able to tell if its viral or bacteria causing the pain.
My daughter had her tonsils and adenoids removed 4 years ago and has gotten strep throat at least 7 times. So my answer would be yes.