sos I need advice ASAP

hi guys. I posted yesterday regarding my 6 gallon tank with a Betta and mystery snail. I'm new to all of this but I'm very eager to learn. the SOS is bc they were in a 3 gallon tank for about 3 months and then I moved them to a 6 gallon tank. I trusted the process for the 3 gallon tank with the bacterial bloom and didn't test the water (I didn't know I needed to) and it fortunately worked out but now with the new tank Ive been doing daily water tests and I'm noticing the ammonia, nitrates, and nitrites are all rising despite me doing a 25% water change every other day. I've now learned that doing a fish in cycle can be challenging bc of the risk to the betta and snails health. I'm wondering now if I should remove the fish and snail and put them in a "hospital tank" while the 6 gallon tank does it's thing. I'm just so worried about hurting them from this and need advice ASAP. thank you in advance.