I made one room into 2 rooms and didn't think about the lighting. It was one room with 2 lights connected to 2 light switches. Now its 2 rooms with a light in each room still connected to the same light switches. One switch is outside of the room and the other switch is at the top of the stairs. Can I split the light for the new room to its own switch or even just remove it from the switch and install a ceiling fan with a chain?

You have 3 way switches. Not easy to split unless you know where the power source originates. If it is hot from a ceiling box, you would convert to 2 switch loops. If it is through the switches, you would need to convert to single pole switches keeping the 3 conductor wire and make 2 hots. Then, convert the second light to a switch loop. There would be no connecting wires between the lights. I am not good at graphics but did draw it out and it could be done. Hopefully our good graphics poster will come along.

Turn power off. Remove switches and describe the wires in each switch
Remove light fixtures and describe wiring in the ceiling. Do not disconnect any wires just look and describe wiring. Call light you want to keep on the switches Light #1. Call the light in the new room Light #2.

Describe like this.

"Switch at top of stairs, one cable with black, red and white wires. Red and white are connected to the brass screws and black is connected to black screw.
Switch at bottom of stairs has one 2-wire cables, black and white and one 3-wire cable with black red and white wires. The white wire of the 2-wire cable is connected to the black screw of the switch. The black wire of the 2-wire cable is connected to the black wire of the three wire cable. The red and white of the 3-wire cable are connected to the brass screws of the switch.
At light #1 there are three 2-wire cables. The white of one 2-wire cable is connected to the white of another 2-wire cable and to the white of the light fixture. The black of one 2-wire cable is connected the white of another 2-wire cable. The black of one 2-wire cable is connected to the black of another 2-wire cable and to the black of the light fixture."

There are a number of ways the lights and switches could be wired. What I have just described is quite likely the way yours is wired.