Court Says I have to Pay Child Support from Arrears but I did pay. Do I need a Lawyer?

Location: Arizona

Been divorced now for 8 years (2016). Two daughters now age 15 and 17. Worked for the county for 1 year and child support was automatically taken out. Got the notice from HR before my first paycheck. After 1 year couldn't handle being so far from kids so quit job and became a sub. teacher. The sub company let me know as well that support would be taken out automatically. Did that for 1 year as I finished a masters degree so I could get a full time teaching job. Got my probationary contract the next year so I was officially a School District employee and they as well notified me that child support would be taken out automatically.

Now here's what is strange. I never told any employer about taking out child support. It just always was taken out after I was notified. I always let my ex know when I had a new job, and I figure she always quickly contacted them or the state of AZ of the change and made sure she got her money. Last month she said she had to file a claim for a Child Support Adjustment and for Child Support Arrears claiming she was forced to by CPS because she was being investigated over her youngest daughter. (I am not the dad, but the guy I accused her of cheating on me with which led to divorce). They were investigating her for neglect. My youngest daughter was there and said her mom told CPS that it was tough to take care of the youngest kid because she doesn't get child support which is true because the baby daddy dropped her right after he found out about the baby and didn't want to deal with her divorce or the child.

So went to court and judge adjusted support amount which was about 50% more. She claims she makes less so needed more money. Could argue but didn't think I wanted to start a fight so figured I would just pay the amount as most of it goes to my girls and they want for nothing. So here are the numbers. I was ordered to pay $871.77 a month when we first got divorced. Based on my salary at Pima County. Even though I got paid half that when I was just a substitute teacher, paid anyway the amount, just lived in a room for two years and ate a lot of Ramen Noodles.

So after the support adjustment, the judge said she wanted to talk about the arrears. I told the judge I have no idea what this is about as it is automatically taken out so make no sense. Ex said she is only getting $804 every two weeks. I honestly know this as I see the amount out of my check every two weeks (802 on my stub. I figured that was just the amount that was figured out and has been taken out since I can remember. Judge asked if I was a teacher and got paid during the summer. I said yes as that was the best way to make sure child support is always taken out. She said she would investigate it and for the moment in the court house wouldn't require arrears, just the support adjustment. Today in the mail I got the official adjustment notice and notice I have to pay arrears in the amount of over $9,000.00 meaning an additional $75 each paycheck till the amount is paid off. This can't be right so I found my year end paystubs all the way back to 2019 when I worked for the school district. Sure enough in deductions it shows that I paid

CLEARINGH0USE CHILD SUPPORT 401.18 10,430.68 so if you 871.77 x 12 is $10,461.24 so I believe this proves I have been paying the correct amount. My question is did I not pay it? Did my employer, the school district screw up and not pay the correct amount? Do I need a lawyer or can I fight this myself, and if I do need a lawyer, what kind? thanks for all the responses in advance.