Ammonia levels

What is the most suggested way of reducing the level of ammonia in a tank? My tank has been going for a year now, as of this July, and all of the sudden, the levels are up from .25 to a 1 or higher. I did a water change, leaving as least 30% in the tank, filling it back up, then changing to about 30% again with a siphon to get any poop or whatnot out of the tank. I bought new filters, but I think I read somewhere that it's not the best idea to change water AND filters at the same time, so I've been waiting on switching those out. I have my axol in a separate tank for now, since he seemed to not be doing so great, but I'm having issues controlling his temp without the tank chiller. I have attached pictures of my tests. 1st one is from 2 days ago before the water change, 2nd one is from today. Not much of a change...

Any suggestions would be great!

Doing water changes will help, but your completely right on not swapping out that filter medium yet. Put some well cycled tank water into a bucket, then simply gently rinse the medium under the water in the bucket. Your filter pads and other ornaments in the tank are the thing that's going to help as they all hold onto beneficial tank bacteria that will help convert ammonia into nitrites, then with other bacteria into nitrates. The nitrates can be removed with your routine partial water changes. Sucking out poop and uneaten food is a brilliant first step to helping reduce levels over all, but the bacteria also needs time to do it's job.

i agree with Genny. not only does the bacteria need time to work but it also needs time to accumulate. the more water you remove, the more toxins you remove, yes. However, you are also removing the bacteria which you need to cycle your tank. you need to find a balance between the two.