What would be signs that amoxicillin was having an interaction with the effectiveness of sprintec birth control?

Not much: Really the only evidence you might see would be spotting,, breakthrough bleeding, or unintended pregnancy. There are no tests or other symptoms. Most people wouldn't even know an interaction was occurring, but it is thought that Amoxicillin may decrease the effectiveness of the birth control pills. Current thinking does not advise backup birth control but no harm in using a condom if concerned.

Pregnancy: Although rare, antibiotics can interfere with birth control. You would not be aware of this until you miss a period. I recommend using a back up method of birth control, such as condoms, when on antibiotics. If your period does not come at the usual time, get tested. Good luck!