How likely is the possibility of infection after neck lift/bleph procedure combined? Is there alternative to antibiotics?

Infection after facial surgery is rare. Antibiotics are often given to decrease this risk even further. It is not unusual, however, to give a reduced course of antibiotics for patients with severe allergies or sensitivities. There is some flexibility.
See the link below for more information on face/neck lift surgery.

A detailed discussion with your Board Certified plastic surgeon would be the next best step.

Thank you for the question.   I think you should discuss the antibiotic plan with your surgeon, as if you have an antibiotic that you have taken in the past that did not give you extreme pain but also covers common bacteria that are found on your skin, you may have a better option available without having the uncertainty of extreme pain.  Either way, infections are rather rare, and not always "required".  Discuss this with your surgeon (this is not an "inconvenience", as nobody benefits from having you in pain), and get it cleared up before surgery so that you are not putting yourself at a risk for complications at a time when you are sensitive.  Good luck!