If the ear hurts when manipulated then you almost certainly have an infection of the ear canal, which is treated with ear drops. Amoxicillin doesn't work for that. Amoxicillin is for a middle ear infection, which causes prominent hearing loss and some pain, but not so much elicited by pushing or tugging on the ear.

I would get started on an eardrop such as Cortisporin Otic or Ciprodex. The only caveat is that if your infection is due to debris in the ear canal you will need to see an ENT regardless to have it suction cleaned. Also, if there is debris or you are diabetic it could be a fungal infection, which would not respond to antibiotic ear drops. If you don't have insurance issues I would probably see an ENT as my next step.