Is doxycycline 100 mg good to take for a sinus infection?

In general no: Doxycycline is not generally a good antibiotic for rhino-sinusitis. If there is objective evidence of a bacterial infection (documented by culture) i would always recommend a culture and sensitivity of the lateral wall of the nose, particularly, is pus is present. Augmentin (amoxicillin and clavulanate) in patients not allergic to penicillin or Levaquin would be my recommendations. But a culture is required to make sure.