How old is your sister? Why do you HAVE to pay for her trip? Declutter and downsize your belongings, sell what you haven't used or worn in 1 year or more. Get a second job. Try the savings challenge (if you have time) where week 1 you put in $1, week 2 you put in $2, so on and so forth, at the end of 52 weeks you'll have over $1000 saved (try upping the amounts if that too little in savings). Save your tax refund and use that towards your trip. Reassess your vacation, sounds like you've set your expectations too high in the amount of time you alloted yourself to save for it.
When you're barely scraping by, it's not the time to be thinking about $5k road trips.
Save $100 a week and you can afford this. If that's hard, simplify your life to drop a bill or two, or see if you can get a better job.
Get a second job NOW. A real job. Not collecting cans and saving change. Work seven days a week.
You have no business spending more money when you already have "more bills than you know what to do with."
Sell some of your stuff or start planning for next year instead. Good luck!