Is it bad for a stye to pop on the inside of my eye?

No. Use some artificial tear to help rinse out the discharge. Then use comfortably hot compresses on the closed eye to help the style finish draining. The style may well completely resolve with the continued use of te hot compresses.
No. A stye comes from a plugged oil gland in the eyelid. Usually you can heat it and express the oil on your own if you are willing to get it hot enough and press hard enough. This time, the stye did it for you. Clean your eye with some water, heat it, squeeze the stye, then repeat. If you have problems, you can see your specialist eye md (ophthalmologist). The medical term for stye is chalazion.