multiplayer Mathematics game need to be transformed from shared hosting to handle thousands of users -- 3

I have a php javascript mysql math multiplayer game that can be played by 5 or 6 at the same time. The problem is : it is hosted by shared hosting, so many people cannot play at the same time as it cannot handle database access. Is there a possibility of involving node.js or socket.io or both. If you suggest going for different type of hosting i will consider. Something like world maths day games where millions play at the same time. Are you good at that? Please advise giving details about whether i should go for cloud or vps. What is the cost? please kindly read this discription fully before bidding.