You don't need a heater unless the tank is at about 12 degrees so you can get rid of it and save your mom some money on the electricity bill
If you can't buy an aquarium "gravel" vacuum you can make your own :happy:
There are some instructions here Just a couple of notes. Use a longer tube or the garden hose so you can drain it either straight outside or into the closest sink and the longer the hose (to a point) the better it works. 2nd note is keep as much of the bottle as possible. The longer the bottle the more sand remains in your tank while the gunk is removed.
Both those products are the highly suspect "Live filter bacteria in a bottle"
There are a couple of problems with them, mostly though it's the question of how do they keep the bacteria alive in the bottle on the shelf? How do they keep the bacteria alive in the bottle with no food? Any food (ammonia, Nitrite) that was added would quickly be used up leaving you with a bottle of Nitrate and dead bacteria. Let's say they don't use up all their food then you will be adding more ammonia and Nitrite to your tank as well.
If they don't add any food for them then at best you get a bottle of dead bacteria that will act as a nice little ammonia source

I don't care what the manufacturers say they have yet to find a way to keep them alive properly and user tests on here and other fish keeping forums I frequent have all shown there was little or no difference in the time it took to cycle their tanks but they didn't do any harm either. I'd also be checking the ingredients on the labels to make sure they don't contain anything nasty. Heaven only knows what the Gel is made of. Most of these things are made for FISH tanks and fish are a lot tougher than Axies

mostly because they have scales to keep this stuff out and off them.
Check the labels against the known unsafe for axie chemicals and heavy metals on the health page of axolotl.org before you add it to the tank. If you think it's safe then it shouldn't do any harm to use the spray but I personally would avoid the Gel until I was sure the gel was safe for my axie.
I have no idea how on earth your levels could still be the same AFTER you change some water. One possibility is that while you were at school the levels rose significantly so changing the water simply brought it back down to where you started yesterday.
I'm glad you water is NO free, how about ammonia free?
OK time to take drastic measures.
Do this in order. It WILL take some time and be a real pain in the backside but you've got to get the levels down pronto.
- Test your water and write down the results. Use the strips if you like for this but make sure you test for ammonia and both nirtites and nitrates. You need to know where you're starting from.
- Change 50% of your water and while you're draining it using a pipe/hose/vacuum look for any rotting plant material or axie poop or uneaten food and remove that with the water.
- Test your water again and compare them to the results you wrote down before they should have dropped considerably, all things being equal they should have halved. If your ammonia is still more than half of what it was then you may very well have ammonia in your tap water. There are conditioners on the market that will remove that for you.
- Now compare them to these numbers Ammonia 0 - 0.5(mg/L), Nitrite 0 - 0.5(mg/L) and Nitrate 0 - 40 (mg/L or ppm) If ANY your newest results are over those ranges then.....
- Change another 30% straight away, don't wait until tomorrow or all the levels will rise again and you'll be back where you started.
- OK 2nd water change complete? Test your water again and compare them to your previous results (should have dropped again and be about 65% lower than your original readings)
- Now compare them to these numbers again Ammonia 0 - 0.5 (mg/L), Nitrite 0 - 0.5 (mg/L) and Nitrate 0 - 40 (mg/L or ppm)
- Still too high do it all again with a 20% water change and keep going with the 20% changes until they are all withing the safe parameters. Preferably NH 0-0.2, NO2 0-0.1 and NO3 0-15
Yes it would be simpler to just change 70% of your water (which is how much of the original water you have actually removed in the 3 changes) at the start BUT as a rule you don't want to be removing any more water and replace it than you absolutely have to

you may only need to do the 1st change, or just 2.
You will now need to keep on top of testing your water
each day and as any of the levels start to climb again (NH>0.4 NO2>0.2 NO3>30) do 20% water changes. It might need to be done daily, or possibly every other day but you will need to be doing the water changes while your tank is still cycling.
It's easiest to keep track of your cycle if you write down the test results each day and note water changes so you can see which chemicals are present and how fast they are rising.
When it's done you will notice a drop in NH and NO2 and the NO3 will rise.
NO3 is the least toxic of the 3 and is easily removed with weekly/fortnightly water changes once your tank is cycled and stable but we need to get you cycled first
Frozen blood worms are messy things and all you can really do to minimize their impact is to rinse them to get rid of the liquid they come with and remove any that aren't eaten.
Most of us use earth worms as the base of our axies diet and blood worms as a treat. They are easy to digest and have everything your axie needs in one convenient wriggly worm shaped package that doesn't pollute your water until your axie poops them out or on the odd occasion that they vomit them back up

If you put them into clean water for 15 mins or so before you feed them to your axies they will purge themselves of what they have eaten/need to poo out and some of the slime will also come off them.