I moved into my moms home in 2008. My mom died in 2016. I filed the forms sent to me by the state of Texas. How do I find out if they’ve dropped the pending nursing home charges?

There’s an exemption for unmarried heir who lived in the house for 1 year prior to death. The answers you did on questionnaire that accompanied the NOI (notice of intent) sent by HMS should have indicated (to them) that there was an exemption to recovery. 

Is property ownership still in moms name and you want to change it? Assessor bills just went out as early payment - I think all counties do early - is due by end of Nov. 
Is it that you got the tax bill and that’s why your ? today?

Have you examined the deed to the house? Are there any liens recorded against it? These are public records so you should be able to go to the courthouse and look them up. Other posters like Igloo should be able to help you much more than I can, but I'd start at the courthouse.