Will cefuroxime (ceftin) effect my birth control pills?

No: Even in 2012, ob/gyns are split on whether antibiotics affect birth control pills....Some say yes, some say no. However, the antibiotics most likely to affect birth control pill efficacy are the penicillins and the tetracyclines (doxycycline). Ceftin (cefuroxime) typically is in a class of antibiotics that will not affect your birth control pill.

No interference: It's an outdated urban myth that antibiotics interfere with effectiveness of birth control pills. They do not, except occasionally with rifampin, an infrequently used antibiotic for certain infections like tuberculosis. Cefuroxime has no effect. See https://www.drugs.com/article/antibiotics-and-birth-control.html