Its tough to get a cluster of misfortunes that involve so much money. Try to deal with each problem on its own, then it won't seem so intimidating as one giant problem that can't be solved. If you stick with a plan of action for each issue, time will heal the wound.
First, I hope nobody was hurt. Did police come, investigate and take statements from you both? Was the other driver given a ticket for not having insurance? The police report usually details who is at fault and its usually the person doing the rear-ending . Your insurance adjuster might take a recorded statement from each of you where you have an opportunity to explain your side of the story. At any rate, assume the worst case scenario and expect pay the $500 to make your car whole. If you aren't considered at fault, let us know later how the insurance company gets the at fault driver to pay your damages.
For the speeding ticket, call or go to the court listed on the ticket and find out what options you have. Procedures are different in each state. In some states you plead not guilty and the prosecutor will offer you a plea bargain and if you agree, you might only have to plead guilty to a parking violation and pay less of a fine. Other courts might require you to attend a traffic school class of several hours in exchange for for reducing the charge to a non-moving violation. At any rate, never just plead guilty to speeding and pay the fine because your insurance company will then be made aware and this will increase your premium even more.
Over the next few months, your going to have to have a disciplined plan to cut back on your expenses to help pay for the almost $1200 in nightmares. Try selling stuff you never use on Ebay, I do it all the time when I'm in a need-money situation. If you work by the hour, see if there are opportunities for overtime pay. It won't be fun, but the consequences of your problems are all financial in nature so they demand a financial action. Your going to have to do without things that you like. Since your case in court might not come up for a while and it usually gives you enough time to pay a fine, the First priority is obviously to pay the deductible. The $500 credit card balance, that can wait where you just pay a little each month. The key is to pay cash for your normal expenses in the mean time to keep that balance where it is. Then when the other two bills have been paid, you can make higher monthly payments on the credit card and eventually pay it off.
All the best.