I have a one year old that has allergies what over-the-counter medicine can I give him. He weighs 20 lbs ?

Check with pedi MD. Though there are several antihistamines available in liquid form only a few have dosing for under 2 years old. Before giving any meds to 1 year old you should check with the baby's pediatrician.
Is it allergies or? Having allergies at 1 yr of age is not that common..Allergies requires prior expsure and seasonal allergies means exposure from prior season and now re-exposing which causes symptoms. It could possibly be from a prolonged cold. Claritin (loratadine) or zyrtec syrup is relatively safe and can help dry things up a bit..If not better in couple of days, consult his doc for an eval...Good luck..