Hi!
As you mentioned it's an antibiotic. Antibiotics help reduce the infection which takes around 3-7 days to resolve. Meanwhile if there is pain which is bothering you then you need to take a pain killer.
The pain will subside once the infection is cleared off if you don't take the painkiller.
Next Steps
Consult your dentist again and ask him to suggest a painkiller for you.
Health Tips
These medications are temporary solution and once stopped taking, the pain and infection might reoccur.
Make sure that you get the tooth treated! Take care.