spider bit lip piercing?

Your piercer will assess your lip and tell you if re-piercing in the same location is viable. Without seeing it, no one here can say for sure. It would just be speculation.

Labret studs are typically better for healing, though some piercer's are fine with downsizing to ring-style jewelry. I'd suggest sticking with labrets until the piercings are fully healed. Less movement, less exposed jewelry, less irritation. You can typically downsize the jewelry within a couple weeks, once all the swelling is gone. All jewelry changes should be performed by your piercer until the piercing is healed, which takes around 2-3 months. While your risk of tooth/gum damage is greatly reduced with proper placement and properly fitted jewelry, the risk is still there.

Ibuprofen and cold foods can help with swelling, yes. Sleeping with your head elevated above your heart will also help reduce overnight swelling.

Personally, I'd rate my lip piercings a 1 on a scale of 1-10. But like you said, pain is relative.

And just so you know...there are no piercings called "spider bites". Those terms (along with snake bites, shark bites, canine bites, etc.) tend to drive piercers absolutely nuts. You can call them a pair of lower lip piercings.