An Arizona-licensed lawyer should review the agreement together with all facts relevant to your termination. The answer to the question may turn on whether the non-compete assurance was given as "consideration" for an agreement to employ you for a certain period. Take all the documents related to your employment and go see an employment lawyer who holds Arizona licensure.
That's not me as I'm not licensed in Arizona. Please consult an Arizona-licensed lawyer to obtain legal advice.
The short answer is: it depends. Many non-compete clauses are designed to expressly survive even if the former contractor/employee was terminated by the former employer/client. That being said, there are numerous other factors to consider, including state statutory and case law regarding non-competes (restrictive covenants). Only an AZ attorney knowledgeable in these areas who actually looked at the language of the agreement can advise you properly. However, just as my informal guestimation, it appears that 3 years is a very burdensome period of time and that would be my first question to the attorney you retain--i.e., whether or not that period is too long under state law, given the context and whether the clause can be invalidated outright accordingly.
I hope this helps.
Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.
As an Arizona attorney, it seems to me that for a non-compete to be valid, there must be appropriate limitations as to duration and geographic limitation, as a court does not want to restrict a person's right to earn a livlihood. My initial impression is that 3 years is too broad, and court's are reluctant to "blue pencil" (i.e. change the terms of the non-compete). Thus, the court would likely strike the provision. Nevertheless, you should contact an attorney to discuss big picture items such as costs of defending a potential suit, liklihood of success with a motion for summary judgment, etc.