I was vomiting for 24 hours and my tongue is coated and mouth is sore with a bad taste. Is this normal?

Likely. Not knowing the reason for your vomiting, hard to say for sure. However, the vomiting brings acids into the mouth and can strain muscles. All these can cause soreness. The coating is a product of the vomiting and your probable lack of tooth brushing/tongue scraping during all of this. Rinse with warm salt wter and clean your teeth and tongue to feel better. Good luck.