I have personally used the duct tape method with success.
As far as the infection, here are some suggestions:
Colloidal or ionic silver. Apply the silver to the splinter area and keep it wet by use of a soaked cotton ball and bandage set up. Better still, mix some silver with gel from the inner filets of a fresh aloe vera plant and apply that regularly and cover with a bandage.
Lavender oil speeds healing immensely and kills germs.
Raw honey. Apply raw honey and cover with a bandage. Raw honey has been used for over 2,000 years to prevent and heal infections. (Raw honey is available in most grocery stores, but the best is organic Manuka honey.) Raw honey applied and left on overnight will often eliminate both the pain and infection by the following morning.
Mix one part powdered echinacea, one part powdered slippery elm and one part powdered cranesbill. Add water to make a paste. Rub on the affected area and cover with a bandage or gauze.
Garlic. Garlic is a natural antibiotic. Rub fresh garlic on the splinter area.Tea. Apply wet tea bags to the cut. The tannins in tea help the blood coagulate faster. Especially good for cuts inside the mouth.
Bromelain (and extract of the pineapple plant) helps speed healing tremendously.