My 13 yo son has a constant colds. doctor said it is an allergy. gave antihistamine but no effect. does he need antibiotics?

Maybe: If he's been congested for many weeks or months, he could easily have bacterial sinusitis that responds to antibiotics. But if he does have an underlying allergic problem, he also needs more intensive treatment for that, to try to prevent a long series of sinus infections.

Allergies ??: If the treatment isn't helping the DX may be wrong. Many kids have prolonged & significant symptoms to irritants in their environment. Smoker parents, hair spray, cleaning fumes, fuel fumes, cooking odors, etc. These all can lead to sinusitis & need abx ocassionally. A lifestyle audit & trial of nasal steroid may be better here, but see the doc & find out your options.