I've read lots of posts here, and never one about giving chicks mineral oil. Sounds kind of wrong, but I don't know why, and I know that is not a very good answer.
I have read that when chicks drink a lot of water they get diarrhea. Could increase its water intake a little. Probably can't force it to drink more, but maybe giving it foods like watermelon, grapes etc.
All in all I think I would wait a few days and see if it outgrows it.
Also if the vent is swollen could you post pix. Maybe you could lube up the vent.
There are solutions for chicken laxatives using molasses, epsom salt, or caster oil, but I think they are used for flushing a chicken of toxins, not so much constipation.
Good luck and keep us informed of how it goes,
Imp