As you know, your pond is not very big. Unless the goldfish are very small (less than maybe 4"), the pond may be reaching capacity. Have you tested the pH, ammonia, and nitrite levels to be sure they're okay?
It is certainly okay to do a total clean out with small ponds when things seem out of control. My page at
http://www.fishpondinfo.com/clean.htm takes you through the steps I do to clean my 153 gallon pond each spring. I save some water so it's not a 100% water change which should only be done in emergencies or as a last resort.
Is the murkiness due to suspended algae, dirt in the water, white (bacteria), or something else? I'm guessing it's algae. See
http://www.fishpondinfo.com/algae2.htmIf it's more milky than green, it could be a bacterial bloom. See a section on that under
http://www.fishpondinfo.com/algae.htm and more on bacteria and the nitrogen cycle at
http://www.fishpondinfo.com/chem.htmI suggest adding good bacteria, more plants, and making sure your filtration is adequate. The pages I've mentioned should give you more ideas so I won't restate them here. Good luck!