I would not let your husband drive if he has the beginnings of dementia. He is probably not allowed to. Maybe your sister can drive you to the appointment if she is on Spring Break this week (?). There are people who drive seniors to the doctors as a hobby in retirement so maybe look online for them in your area? Call them and explain the multiple emergencies.
I did something to my knee on a walk down a slight slope in the forest known as Pine Hill and didn't go to the ER. It hurt when I put weight on it but not enough that I couldn't walk but I needed a cane so I bought one, I think. My doctor suggested I see a physiotherapist. I went. They knew what it was and it wasn't a torn or broken anything and gave me some exercises to do. I had about 3 or four sessions. Then I was healed and no longer needed a cane. Since I bought the cane on my own I apparently used it on the wrong side but that worked for me. I would definitely go to a specialist. Listen to what feels good for you and your body. Maybe having a third person drive you is good if your husband has dementia and you need to see your own doctor on that trip.
My sympathies to you and all the issues you are facing. Take care of you.