You can use both, but drive would sound better with "by". " I am about to pull up to your house." "I'm about to drive by your house to pick up my game."

“Drive up” is fine. It could be used like “pull up” but not always. Businesses like McDonalds and banks can have “drive up windows”. You drive up to the drive up window and conduct business from your car. “Pull up” tends to be a smaller movement and more focused on positioning your car. Pull up a little closer to the car in front of you. You can’t stop here. (Not drive up) Pull up to the first window and pay for your meal. Drive up to the first window and pay for your meal. Both are ok but I’d use “pull” if it’s close. In some states, emissions tests are required. In my state, you just drive up to a testing bay and they analyze your exhaust on the spot. (Not pull up, you’re not talking about positioning your car.)