Can GERD cause tightness at the bottom of your throat? Can it also cause the feeling of something stuck at the bottom of your throat?

Maybe not just GERD. Further evaluation is key to determining if your symptoms are reflux-related or not. Also, if reflux, is it acid or non-acid material that is involved? Sometimes, pulmonary, ent, or dental issues are at play, ; sometimes dysmotility or gastroparesis is the issue. Are you sure your acid blocker dose is sufficient ; that you have been compliant with behavior ; diet restrictions to minimize gerd?
Yes. These are very common symptoms of laryngo-pharyngeal reflux (LPR). This may be the result of strong acid from the stomach coming high up and effecting the back of the throat with a common symptom-of a lump in the throat. The problem is often seen by an ENT doctor but I believe the definitive diagnosis and treatment should come from a GI specialist.