Can I get an infection from a novocaine injection? Gum grafts look fine but my check is swollen and hard. Am taking amoxicillin.

Unlikely . It is highly unlikely to get infections from injections. Needles are kept sterile and the antibiotic you are on should cover most common oral infections. If your symptoms persist I would recommend calling the health care provider that did your procedure.
Cheek swelling. Depending on the type of injection you received, it's possible that you have a hematoma. A hematoma is caused by the injection tearing or passing through a small blood vessel, causing blood to pool in the tissue. This is treated by applying an ice pack for the first 48 hours, followed by moist heat. Call your dentist for an exam and explanation on how to treat the swelling.
Contact dentist. Immediately or go to ER if can't reach dentist. You have an infection that the amoxicillin is apparently not taking care of. .