API Freshwater Master Test Kit is a great one to use! If you don't want to shell out for that, API do single ammonia and nitrite testing kits. You need to make sure you at least have test kits for ammonia and nitrite.
It takes about a month to establish your filter. As you already have fish in the tank you need to test your water
daily and do large water changes (50-80%) to get the ammonia and nitrites to zero. After around a month you'll see the levels naturally lowering as the bacteria start to remove those chemicals for you.
Another thing to remember - small fish do not equal small tanks. I'll be honest and say that while tetras like neons, glowlights and the like are fairly small fish (under two inches when adult), they still need large groups (6 plus) and quite a bit of space to shoal, explore and race around. Ideally you would be looking at 45 litres as a minimum size for these fish - that's 10 imperial gallons.
The small fish that do well in small tanks are the super tiny ones like micro rasboras. There are other small-ish fish that don't need the large groups (like bettas, guppys, some species of small gourami, etc) that would be OK in a 5 gallon tank
in the right numbers (i.e. 1 betta OR 6 micros OR 4 guppys OR a pair of sparkling gourami)
Too-small tanks and over-crowding cause stress and sickness which can strike at any time, and all the medication in the world won't help when they do strike.
Sorry to be the bringer of bad news! It's important to us that your fish are happy and stay healthy =)
Read this!