Hi Omar, Welcome to Fish Lore
Sorry for the loss of your fish, I know it's hard.
With your readings, you need to do daily water changes until you get the ammonia and nitrites down to 0 with some nitrates showing.
Next time, just rinse the filter pad in old tank water and re use it, unless it's really falling apart. It holds quite a bit of benefical bacteria and you don't want to throw them out.
I've opted to not use carbon, it expires and can release nasty stuff back into the tank.
Given your readings, your 10g would do better with fresh treated tap water.
Was your tank cycled at some point? How long have you had it set up?
Good luck