do you have a home and garden centre somewhere near? or a hardware store, or some such thing? what i'm getting at is they sell bags of play sand for about $3-6, depending on the size of your tank it could do for awhile. my 20G tall uses about a bag to a bag and a half, and that works for my crabbies, as the largest is a medium size. $3 isn't to hard to come up with, (couch cushions are great for change lol) and if the store is within walking distance you could always grab a wagon and hoof it.
no one wants to see you leave, all we want to see is both you and your crabbies happy. in a pinch, if you have a playground near with sand in it.... (i'll probably get roasted for this

) you could take said wagon and yoink a bit of sand (just make sure to bake it first!!) and be sure it's clean.
hope this helps!
just a thought too...maybe you could ask your mom if there are any chores you could do to earn the money, as i'm sure she will appreciate the maturity of this (i'm a mom too, i know how it is

). I'm sure she doesn't want your pets to suffer. if you show her that you are willing to work for the care of your crabbies she may relent.