You do need test kits, even if they wont help with your water cloudiness problem.
The absolute minimum kits a fishkeeper should have are: Ammonia, Nitrite, and pH. These readings should be taken whenever any sort of trouble arises in your tank. Rising levels of ammonia and nitrite usually mean that problems are on the way. If you can spot them before it gets out of hand, you might be able to save yourself a lot of time and worry.
Others that are nice to have, and often come as kits with the 3 above are: Nitrate and water hardness (GH and KH)
Even without kits, people may be able to help you. How long has your tank been setup? How long has it had fish in it? What fish are in it? Is the tank cycled? How many gallons is it, what substrate are you using?
As you can see, it's best to give the people here a general summary of your tank