I accidentally cut my eyelashes can I use oil to help them grow faster?

Thank you for your question. Castor oil is found to be effective in growing and thickening eyelashes as well as  preventing them from breaking. We do not have randomized control study to support that but it has been very well known fact from extensive experience. 

There's some stuff out there that may give you limited results, but they should grow back over the next few months without any intervention. I'd suggest just waiting it out.

Eyelashes have a 6 week growth cycle.  They won't take long to regrow on their own.  Just be patient.
Note though that there are now solutions like Latisse and similar which will speed and thicken eye lash growth, but these do require a prescription.