Hello Julie, and thanks for dropping by our little Forum w/ your questions and concerns...
Unless otherwise specified, most builders will have the painting contractor use inexpensive materials; they're not all poor quality, but they're certainly not the best. The paint sticking on everything except the walls could have a lot of causes including, but not limited to the grade of paint used.
The only 'protective coating' to use would be a new paint job; one using a higher quality paint such as Benjamin Moore. You can hire a pro via a professional paint store recommendation, or do it yourself. If you decide to do it yourself you'll find the pros that frequent this Forum will be more than happy to guide you along. We'll cover it all: paint selection, prep, application etc....
John