Hello,

Last night, I turned on my ceiling fan with the pullchain. The pullchain stuck on. I pulled apart the housing and removed the casing, but it appears the pullchain is completely stuck. Do I need to replace the whole casing, or can I fix the one I have?

You can try replacing the casing as you essentially pulled the other one out and broke it.

What make/model fan is it? What does this pullchain control, the light or the speeds? How many speeds?

Sometimes pulling it harder will cause it to snap back, other times it will break. If it won't unstick or it breaks you have to replace the entire switch, see:

Ceiling fan pull chain replacement and repair - Ceiling Fans N More