What happens to the pressure of the air inside the balloon if the volume remains constant if the balloon is heated?

Pressure increases.

Take a look at the relationship:

PV=nRT

R is a constant. n is the amount of gas, which would be held constant in a sealed balloon. So:

P1 V1 / T1 = P2 V2 / T2

1- before

2- after

This algebraic equation can help predict the outcome of other cases as well.
taking just the balloon first, it is a solid body(flexible), on heating it undergoes cubical expansion, so the first thng that happens is the container(balloon) expands so untill a particular expansion of it the volume of air inside increases(gases dont have a fixed volume) they occupy the area they have .