Willa priorDWI from another state effect my newDUI charge?

By virtue of several intra-state agreements or "compacts", most states report an out-of-state DUI to a home state.  Therefore, NM would have reported your DUI's to AZ.  Even if you were a NM resident at the time of your convictions, AZ would have contacted NM when you got your AZ license.  So it is a virtual certainty that AZ has your previous driving offenses on your record.  There is something however called a "look back period" which can help in such a situation.  This is the amount of time that a court will look-back into your driving record for the purposes of sentencing.  Unfortunately, in AZ the look-back period is 7 years.  Therefore, since your first 2 convictions were in 2007, this latest offense will be considered to be your 3rd  (assuming that you are found guilty).  

Under the circumstances, jailtime is involved, so it is advisable that you have legal counsel.  A skilled DUI attorney could potentially get the charge dismissed on a technicality (or possibly get it reduced).  For example, they could challenge the accuracy of the breathalyzer test, or the accuracy of the radar, if applicable.  They could also challenge any procedural improprieties.  They could possible even win an acquittal at trial.  Choose one that practices in the court in question.  They will have local contacts within the system that could prove invaluable when negotiating with the prosecutor on you behalf, or pleading your case before a judge.