It sounds like there might be an infection. Contact your dentist. they will probably want to x-ray to evaluate the tooth. A root canal might be recommended. Good luck.
There is a very slight chance that this chip could soak up stain over time but if the chip is very small your dentist may be able to polish it out and prevent the staining from happening.
Tooth-colored bonding material is a quick and inexpensive method to fix a chipped tooth. Avoid home remedies as anything painted on the tooth could be potentially toxic.