I think you don't need to worry about anything but ammonia and nitrites right now. After your ammonia spikes to 2ppm or higher and goes to 0 you need to watch your nitrites until they go to 0. At this point I don't think your tank cycled at all with only putting in one shrimp for a 300 gallon tank.
The following you can do to test your cycle. If you add the ammonia and the ammonia and nitrites both go to 0 after 24 hours then you are cycled. If not let it run the cycle as I've laid out below.
If I were you, I would wait until you get the test kits, then dose pure ammonia that you can get in the cleaning section of most grocery or hardware stores. You want ammonia that has no additives. Being scent free is a good indicator but shake the bottle, if it foams up it has additives, if it doesn't that is the one you want.
Then dose ammonia until you get 2-3ppm if it goes over that's ok it will just take longer to cycle. Then all you have to do is wait for the ammonia to go to 0, then nitrites and finally you can test your nitrates when your cycle is complete and then do a 50% WC, but do not do a WC or add anymore ammonia until your cycle is complete. Once complete dose ammonia one more time to 2ppm and then test after 24 hours. If your ammonia and nitrites are 0 after 24 hours your tank is fully cycled. This second dose of ammonia is to test your cycle.
This is how I cycle tanks and it works very well and is faster than some other methods like adding shrimp or feeding fish food daily until the ammonia is present, this can take a while.