Is a green booger and bloody nose in a two-year-old a sign of infection?

Yes most likely: If the congestion has been longer than 10 days and there is night or early morning coughing the bit can be a bacterial sinus infection. If its less than 10 days then it may be a viral infection. Nose bleeding can happen in either case. Also one must make sure there is no foreign body.

Color in drainage: The color of any nasal drainage will be caused by the metabolic waste if germs in the mucous. Any mucous in the nose will begin to color within hours of its production due to common nose & throat germs that feed on the mucous. Add that finding to two weeks of drainage, point tenderness over cheeks or forehead & fever @ 2yo & you probably have a treatable infection. Less=cold or allergies.

Possibly: It may be a localized infection just in the front of the nose or a more generalized infection of the nose and sinus. Be careful not to clean the nose too aggressively as this can actually cause trauma making the nose worse. I like gentle cleaning and the use of an antibiotic ointment like bactroban (mupirocin) or bacitracin. Do not use an ointment with neomycin as this can cause bad skin reactions.