There is no reciprocal healthcare agreement between the UK and the Jamaica, so it is vitally important that all travellers to the country take out adequate medical insurance before they go.
State healthcare isn't up to much, but the private hospitals accessible with medical insurance are fairly good, although for very severe conditions they will normally send you to the USA (make sure your travel insurance covers air ambulance extraction).
Most tap water is drinkable in hotels, although you should stick to bottled water elsewhere.