[Symphony.]

First off, let me say I'm sorry you and your sister are going through this. Depression is unbelievably hard on those who have it, and to find out a loved one might be struggling with it must be devastating.
I would definitely talk to your mother first, maybe show her the journal. But here's the truth- whether your mother says she read the journal or whether she makes you own up to it, your sister will probably angry. But would you rather have your sister not be angry at you, and suffer, or have her be angry at you but recovering? The anger won't last forever, and once she recovers, chances are, she'll be thankful you went into her journal.
I know you're scared, but I do think it's important someone else finds out, someone that you trust, so your mother is definitely a good person to talk to. Make sure your sister isn't around or isn't in the house, because it might be harder if she catches you two talking about it beforehand.
Like I said, either way your sister will (most likely) be angry that whomever she is told looked into her journal. But don't be so hard on yourself- by "snooping," you've potentially saved her.
About the economic troubles- does your family have insurance? Maybe they'll be able to find a psychiatrist their insurance covers.
Hang in there, and best of luck to you and your family.