Car registration dilemma – HELP!

I moved from another state and am trying to get my vehicle registered in Texas. I started a new job right away that is M-F so I didn’t think I would be able to get into an office. I emailed the Harris county office and they suggested I file by mail (not letting me know the extended processing times)… I submitted by mail but now I received a letter from my previous state saying that since my insurance has changed they are going to cancel my registration. I’m panicking because my out-of-state registration is going to be cancelled before I get my Texas tags and I don’t know what to do!