I accidentally washed my face right after 2 hours of application of the chemical peel.

Even though I don't know what type of chemical peel your had, washing your face should not diminish the results.  Most agents used in chemical peels can not be washed off or neutralized after they have been applied.  Once it is on, it is on and you should get the desired effect.  If you have any problems make sure to report them to your provider.  Also, make sure to follow their post-peel instructions.  I hope this helps.
Dr. Smart

Depending on the type of chemical peel you've had washing your face after 2 hours should not alter the peel's effectiveness.  However, you need to contact the provider who performed your peel for details and instructions.  
Best,
Dr. Huo

There is different types of chemical peels and post-treatment instructions can vary, but most chemical peels will not be affected by applying water to the treated area. In fact some are neutralized by the provider with water until the stinging, burning sensation is stopped. For specific instructions to the type of peel you had I recommend you call you providers office.

Best-
Alex Khadavi M.D