Seating tires on the rim.
I use the following method to seat a tire on the rim. I am not suggesting you use it, and if you do, I take no responsibility for any mishaps that may occur. While I have never had a mishap, the possibility does exist, particularly with high pressure tires.
But first: If you are dealing with a Schwinn bike you need to determine if the rims are American made tubular type. If they are marked "Schwinn", you must use a tire specifically made for Schwinn tubular rims. If they are marked otherwise e.g., "Schwinn Approved", you can use a non Schwinn tire. Even though the tire size marked on the sidewall, there is a difference in the bead diameter of Schwinn and non-Schwinn tires.
It is often difficult to get a tire to seat properly on the rim all the way around. The first thing I do is to center the stem so that it is perpendicular to the rim. Then I push the stem into the tire so that the tire bead seats properly. I then determine the proper tire pressure shown on the wall of the tire. With my safety glasses on, I pressurize the tire to the recommended pressure and check to see if it is seated properly. There is usually a raised line on the tire at rim level that can be used for this purpose. If the tire didn't seat, I over pressurize the tire 10-15 PSI. If the tire still doesn't seat, I deflate it completely and go get some of my wife's liquid dish soap, a glass of water, and a small brush.
I Put a few squirts of soap in the water, mix and brush the soapy water on the bead of the tire all the way around on both sides. I Use the mixture sparingly since I don't want too much water to get inside the tire. Now I re-pressurize the tire. If the tire pops out to the rim at the recommended pressure I'm through. If the tire did not seat, I add another 10 to fifteen PSI. If it still doesn't pop out I try to work it out with my thumbs by pushing the tire wall up from the rim in the low area. The last thing I do is to make sure the stem is perpendicular to the rim and pulled all the way out of the tire. These methods usually work but occasionally I have had a tire that refused to seat.