If this is a true artesian well the water will flow out the top, but there should be very little if any pressure. If the water is flowing out when you remove the cap, it will be hard to get chlorine to go down where it needs to go. You really need water to flow back down the well so the chlorine gets forced out into the water formation to get to where the problem is.
Some artesian wells do not flow, and you should be able to get chlorine down where it is needed. You really need to chase the chlorine with enough water to force it out the bottom of the well where it is needed.
