2yr old given two drops oflaxin for pink eye. Hives within ten min of drops and lasted 5 days. He also had hives after amoxicillian. Antibioticallergy?

Very unusual. Although not impossible, hives from an eye drop is unusual since very little of the medicine gets absorbed in the body. Nonetheless, we should presume an allergy reaction & follow up with your pediatrician or allergist for additional testing. And to clarify, it would not be an allergy to antibiotics, but an allergy to quinolone antibiotics and Amoxicillin (although rash may also be a side effect.
Allergy. Most likey a topical reaction to fluoroquinolone drops. Would not use again in future.
Possible allergy. Assuming your child was not taking any other medications or was exposed to something else at the same time, it is best to discontinue the eye drops and have him seen by the eye doctor immediately. He may be allergic to fluoroquinolone antibiotics or one of the other chemicals in the medication, and should be tested by an allergist to be sure.