I'm having allergic reaction to antibiotic (hives and itching). Can I continue my antibiotic treatment if I pair it with antihistamines?

No. An antihistamine would mask some of the obvious signs of the allergic reaction while other more dangerous mediators remain unchecked. There are almost always good alternative antibiotics.
No. Please stop the offending drug right away, call your doctor for treatment of allergy symptoms and for alternate antibiotic if you still need one. If you do what you suggested, you can risk having a more seious reaction and antihistamines will not help but would rather mask the initial milder symptoms, and your condition will be totally unpredictable , wish you wellness.