This is Samuel and I will discuss this and provide you information in this regard
I am sorry to hear you have been terminated. Your appeal process will come from within the employer's policies. If they provide for no appeals process, then you have none.
I suggest, that you should apply for unemployment. But that you consider having an independent drug test done now to show that you never had drugs in your system because if the employer is going to oppose your unemployment it will be based on your tests. So if you can show with your own independent testing that there were never any drugs, you can collect unemployment - and also you may be able to have a wrongful termination
lawsuit because of a faulty drug test. So in that regard, once you get the test, get the unemployment granted, I suggest you consult with a local attorney to discuss a wrongful termination suit
I suggest you can contact your local hospital and they can give you referrals to a drug testing lab for your purposes.
Please note that I can only provide information for what you ask. In that regard, if you have other questions or need clarification, please let me know here. Otherwise, I would appreciate a Positive Rating as that is how I get credit for my time.