I ordered a game on Amazon on the 18th and the estimated delivery date is tomorrow. UPS tracking says Billing Information Received. Will I still get the package tomorrow?

That depends on several factors. When you ordered it from Amazon, did you request 2nd day delivery or overnight. I ordered a package from Amazon that was second day. When I got the delivery confirmation from Amazon, I clicked the link and read that billing information was received. But the next day UPS deliveered my package.

The possibility of you getting your package the next day is great indeed. Again, it depends on what type of shipping you requested, and how busy UPS is.