If the bumps go away when you do water changes I'd be worried it was something in my water. The dechlorinator you have will remove chemicals from your tap water and will help to get rid of ammonia (is it Prime by any chance?) but the dechlorinator won't monitor the rest of your cycle or regulate it for you - this work is done by your natural bacteria and by you doing water changes to remove any excess ammonia, nitrites and nitrates.
I really would push for a testing kit - I know your pain. When I got my axolotls, my parents laughed at me because I was doing all these weird things that they never did with their fish - storing and dechlorinating water, testing it, buying Polyfilter at £12 a pop, cleaning filters, etc - but my Dad's fish often died spontaneously and when he saw how healthy and well my axolotls looked he began to respect my (limited!) knowledge and began to ask me for advice and to help him with his tanks. Now I have him testing his tanks every week, doing regular water changes and diagnosing illnesses and problems BEFORE they ravage his tanks. He's realised that problems are preventable now. Failing that, I don't know how old you are, but I started working at 16 (don't get me wrong, I hated it at first) and this meant I could buy what I wanted with my own money, so if you're old enough and can find one, this will remove it completely from your parents' jurisdiction. Your money, your choice what you spend it on.
I don't mean to be a battleaxe about this, but a test kit is essential really, especially for a creature so sensitive to water quality. If you really, really can't get a test kit, can you get a sample of your water to a local Fish or Aquarium shop? They sometimes test for free!
