"b) Would not the college own the IP anyway?"

Only if OP were employed by the school for the creation of that IP. University research grants often have a commercialization clause in them that requires some involvement of the school in the event a product results from the research...but independently funded projects certainly do not fall into this category.

a) The professors realized midway through the semester that they would need outside help to do this and gave him permission to use me.

b) I really don't know

It's my understanding that the copyright for schoolwork always belongs to its original authors; it does not become property of the school.