Burning eyes 9 hours post botox injection in between brows. Will my vision be affected? Will I have droopy lids?

Botox injected in the brows would not cause burning of the eyes and should have no bearing on increased risk of ptosis or blurry vision.  It is likely a coincidence, but make sure you are evaluated for the cause.  It could potentially be related to a product applied such as a numbing cream. 

It is unlikely that the burning in your eyes that you are experiencing is realted to your Botox injections.  However, if you are concerned, call your doctor.  Doctors should always be available to discuss concerns of their patients.

The Botox injection you had is not directly related to the burning of your eyes.  Since you are very upset and it is interfering with your daily living you should contact your plastic surgeons office and inform them of your concerns.  It takes a few days to notice a drooping eyelid if it in fact occurs.  I hope this helps.