My back left molar has cracked and there is a massive hole there where the tooth used to be. i think i swallowed it and may need an antibiotic.

See a local dentist: You can't get medications from this forum, and meds will not repair the rotten tooth. It may need to be extracted. Please don't wait to have serious pain or an infection.

Broken tooth: If you swallowed part of a tooth your stomach acids will kill any pathogens associated with the broken part of the tooth. The rest of the infected tooth, the part still in your mouth, is spreading infection to the rest of hour body via your blood stream, and antibiotics may be required until the tooth is treated or removed. But not here. You need to see a Dentist for Rx and to plan treatment.