Glad you are okay. Its amazing how cars have become safe now. From the picture, there was some speed, 15 years ago you'd be in a hospital or worse. Have yourself checked up tomorrow, sometime it takes a day or two for pain to develop and you may retain debilitating conditions (don't ask how I know...)
Now, you have learned a valuable lesson. Being right, having the right of way doesn't matter. No matter what, nobody's perfect, even good drivers do mistakes occasionally, thus someday somebody will do something stupid in front of you. It is just part of your mission as a driver to be able to avoid them (conversely someday you'll be glad that somebody was aware enough to avoid you and save the day). The fault is theirs, but with more awareness (by adapting speed to surrounding conditions and a capacity to "read" distracted drivers and suspecting anything that has a brain as a potential danger trying to suicide on you), an accident often turns into pointless rant against stupid drivers, or in the case, some sort of misogynistic comment on blond cheerleaders capacity at the wheel
The case for the car being safe is made. You walked out of it and the picture is not pretty. With that money you can get the same car, more or less.
Should you get a Corrolla ? Actually a Corrolla is plenty fast. Well enough to get you in danger if you don't take responsibility for your safety and act defensive (no, defensive driving is not driving like gran'ma, its looking around at what's going on and being ready). Now, insurance premiums are gonna be tough on you if you get part torts. You could maybe consider some driver improvement program to get them to normal, good way to improve skills, often its fun, and you may save on the long run (and make your mom happy).