Linda,
First, breath and be easy don't let this process stress you out or Carol for that matter. Your medical facility is still going to do treatments etc, please do not concern yourself there. It is standard procedure for SSA to qualify an applicant for Medicaid the same time they are qualifying them for benefits. I went through this process...I know and can relate to the situation.
The facility treating Carol understands this process as well and if they've agreed to treat Carol and bill the city's medicaid program (which pays the same rates) they'll continue treating Carol and bill State Medicaid which will backdate billing to when the city discontinues to pay. Everyone involved in this process has danced to this song before...except Carol and you.
I can detail how this whole process goes, I lived it and can tell you that all of my dr's, pharmacy etc..knew the game and were well versed on how to play it to get paid.
I've never been denied treatment, meds anything. I knew that before I had any procedure done or any prescription filled that there was an approval process but 95% of the time it was just billed out. The other 5% I had to wait a little bit if the script was outside what Medicaid would normally pay for (an authorization would be needed from Medicaid, which always was approved) or I would have to get pre-approval for surgery outside my state, both from Medicaid and the hospital doing the surgery (if they accepted Medicaid or not) again, never had a denial there, just had to wait for approval.
I hope this has eased your mind a bit and that when you read this you will have a better day tomorrow and at least enjoy one day of the weekend.
Keep those spirits up!

Eric