Is it bad when a stye bursts inside your eyelid and what is the solution to the problem?

Probably not: This is most likely a chalazion, which is different from a stye in that it is not an infection, but a backed up oil gland. In either case, the eye can be gently rinsed out and treated with a hot compress.

Not bad: It is not bad, and usually good when the stye bursts, it will then drain and go away usually. Use warm compresses to the eye lids and keep the purulent material cleaned from the eye. A tye is not an infection but a clogged oil gland.