TheKoiMaiden makes wonderful points!
I just want to emphasize that we're NOT trying to pick on you or accuse you of trying to hurt your fish. I can see that you care for them, and want to do the best for them. We're just trying to help you learn what is the best thing for them, so you can aim for that.
It might not hurt to ask around to friends and family to see if anyone might have a storage bin you can borrow. When I was using one, I found it in my parents' basement holding baby clothes. Its possible that someone could let you borrow one, especially if you provided them with some cardboard boxes (that can be found for free) in which the can store the former contents of the bin you're borrowing. Its an idea!
Also, a possibility might be looking into used tanks and equipment now, or when you've saved some money. Some pet/fish stores, especially independent ones, sell used equipment. Also, you could try looking in the classifieds. Often people grow tired of their fish stuff and sell it for super cheap. craigslist.org
is awesome for this, if you're in the states.
Oh, and I just thought- there are some things you can do to help supplement the cycle. If you know anyone with an established, HEALTHY tank (no history of disease) you can take some biomedia (i.e. anything that grows beneficial bacteria on it like substrate, filter media, decor, etc) and "seed" your tank with that beneficial bacteria to help jumpstart/supplement your bacterial growth. It must come from a healthy tank, as you can't clean it in any way or expose it to chlorinated water. You just take the biomedia from their tank, keep it wet in tank water, and put it in your tank as quick as you can.
Does your tank have a light? If it doesn't, do you have a desk lamp that you could shine into it? If so, we could suggest plants that would really help with the cycle. There are a handful of plant species that are exceptional at sucking up Ammonia before it has a chance to harm the fish. So let us know if this is an option for you, what kind of light you have, and we can tell you specifically which plant to get. (Not all plants will help your situation, so we'd have to plan it out so as to not waste your money.)
Speaking of which, just today I bought a clip-on desk light from the thrift store. I'm using it for hatching baby brine shrimp to feed to my fry, but the same kinda thing would be ideal for your situation. Oh, and THAT reminds me that I've seen tanks for sale at thrift store before. Who knows if they hold water, but they can easily be re-sealed with $7 worth of silicone sealant and some elbow grease. Re-sealing a tank can seem intimidating, but really only requires some research and a can-do attitude.
I'm really pulling for your little fishies, I hope they can heal up and be healthy!