Hi drum_stix,
Antibiotics can only temporarily subside the symptoms because the infection is not going to go away as long as the root tips are there. An example would be.... you a get large splinter in your hand and as you try to remove it, some pieces break off and you push them further into the skin. Dr gives you antibiotics.... the soreness subsides so you leave it. One day out of the blue, your hand hurts, it's red and swollen. What do you think it could be?
Did you see an oral surgeon or a general dentist for the extraction of that tooth? It really would be best to see an oral surgeon for the removal of the root tips as they are more experienced in that type of oral surgery. If it was an oral surgeon that removed the tooth and left the root tips, then for obvious reasons, please see a different oral surgeon.
Please check back to let us know how you are doing.