I Had A Tick Head Get Stuck In My Dogs

I had a tick head get stuck in my dogs skin, and I was digging around it to get it out... then found out that would worsen the chance of infection. It says to use an antibiotic on the wound.... can I use this neomycin and polymyxin B sulfates, and Bacitracin Zinc Ophthalmic Ointment, USP By Akorn on his wound?