I signed a contract to work at a PR Firm. I decided to leave after 10 business days due to the environment. May I collect payment for the 10 days work

Any answer here will depend on the contract you signed.  If you were contractor and the contract says are you paid on monthly basis, then you may not be owed the money.  I think that would be unlikely, however.  So, you should have attorney reveiw contract -- or, better yet, just file small claims court action.  It is easy and you can do yourself.