Hey there! Welcome to the family!
Don't feel bad ... there's a lot to digest in this hobby and it can be overwhelming.
The term "cycling your tank" refers to the process of building up a sufficient colony of nitrifying bacteria that can affectively process ammonia into nitrite, and then nitrite into nitrate (these two steps actually require different strains of bacteria). This is a critical step that you MUST go through before your tank is safe for livestock. All livestock give off ammonia through respiration, and ammonia is also produced throughout the natural decomposition of fish waste and uneaten food - therefore, if your tank has NOT completely cycled, it will not be able to process the ammonia - which is highly toxic to your fish. So if you add fish before your tank is cycled, the ammonia levels will just build up until it eventually kills your fish.
Cleaning the rocks like you did will not prevent you from having to undergo this problem.
Paradoxically, however, to START the cycle you must first ADD a source of ammonia to the tank for the bacteria to have something to feed on (and thus multiply).
So if you've had your tank setup and running but haven't seeded the cycle with an ammonia source, the cycle won't start. So the fact that you aren't measuring any ammonia levels already could simply be because there were never any there to start with!
The fact that you are measuring some nitrites and nitrates is most likely a reflection of the quality of the source water you used.
SO - do you have ANY livestock in the tank today? Or, before you added the Dr. Tim's did you first add a source of Ammonia?
If not, you may still be at square one.
If you have been adding ammonia or have some small amount of livestock in the tank already, you may be further along.
Can you please elaborate?