What's it smell like?, rotten eggs (sulfur), does it smell kinda "swampy" or is it a metallic smell?
You say the hot water smells more, Im guessing, sulfur.
I wouldnt just keep pouring clorine down. Clorine is good to get rid of bacteria in a new well and new house plumbing, you should always run some clorine down a new well or through the plumbing of a new house to kill the bacteria in the pipes, but in the long term, you need to address it with UV light or filters.
You can use a charcoal type filter to get rid of just about any type of smell.
Sulfur, while it smells sickening, in moderation, isnt bad for you.
Metals, as well as limestone, (hardness) in the water can be filtered out also. or you can use a softener to filter and change the hardness characteristics of the water. Iron and limestone arent bad for you either.
Either way, give up on simply pouring clorine down it and have it tested so you know what kind of long term fix you need.
You dont need to spend a bundle testing it for everything under the sun unless you suspect that its contaminated with something like lead or fertilizer then you can have it specifically tested for those things. Definately have it tested for bacteria though. You can figure out most of the common well water ingredients on your own. Iron leaves stains, limestone leaves white scales and sulfur smells.