I shaved a small part of my eyelashes, will it grow back and if so how long?

Eyelash gone, don't worry, it will grow back; if there was trauma to the area, there will be a one month delay and then it will grow back at 1mm per week; So you must be patient; you may want to get some Latisse to stimulate quicker growth.

Hi there and thank you for the inquiry,
Latisse is a great product that can help grow your lashes longer, thicker and darker over the course of several weeks. You can expect to see noticeable lengthening after 3 months and also please note that your lashes will eventually regrow to their natural length with or without eyelash lengthening products. Consult with a cosmetic plastic surgeon for an in-person evaluation. 
You can try to wear individual eyelash extensions or false eyelash strips for an immediate solution.