I had exactly the same issue last months. The smart phone Micro SD card also needed to be formatted after attaching to computer. But, considering about the inner remained data, I just cannot force myself to format it right now. Therefore, before formatting this card, I had tried many ways recommended on the internet.
Luckily, after trying many data recovery software, I finally viewed my card data on my computer again. It was awesome. Did you have any luck?
If you are also interested, here is an article that I have used:
It could also give some helps.
In the future, upload all your card pictures to computer timely and also prepare data backups, just like me.