This is probably ADHD-type inattentive aka ADD. Same thing happened to me. Vyvanse/Adderall solved my problems. I also made some lifestyle changes and stopped caring about shit that doesn't matter(for example, facebook, whether other people would judge me/think of me as a failure..etc). I got re-admitted and now I'm kicking ass in college.
Read up on ADD/ADHD. I know it is overdiagnosed and there are many critics who believe it is not a real disorder, but when you actually have it, you know how humiliating it can be. The disorder is due to a lack of dopamine or overabundance of dopamine transporters in the brain or something like that. It is a chemical imbalance in the brain. This is a fact. It's been proven over and over again. If you are extremely shy or have social anxiety, that can also be related to dopamine. Many people including myself, get diagnosed with the inattentive type in college or adulthood, because they've been able to cruise through primary and secondary school by being very smart but not needing to do much, and from having a support system from a stable family at home. Once you get out of high school and have to fend for yourself, ADHD type inattentive rears it's ugly head. It's very difficult to adjust when your brain circuitry isn't right.
I suggest you get tested for ADHD/LD. Do this first. Your university's counseling center or a doctor should be able to get you referred for one. Call immediately, because it will take a few months before getting the referral. When I did it, it turned out to be some IQ tests that took several hours over the span of a few days, but they were very accurate in showing what was wrong with me. Sustained attention was very poor. My doctor put me on Vyvanse and I can finally do things a normal person would do. You can build a tolerance to the drug, but if you know your body well, you can use it effectively regardless. And you have to eat a lot and stay hydrated, but you'll get used to it. I know stimulants seem scary, but they really aren't that bad. They are the most effective treatment for the disorder. There are other dopamine boosting things out there, but they do not do much for ADHD sufferers compared to stimulants.
Take classes at a community college, keep the gpa up, and if you want to reapply to the same place, then talk to whoever is in charge of that stuff and you should be allowed to petition. You will probably have to write an essay explaining what happened and how you solved your problem. Only try for readmission once you've solved your problem and shown progress at a community college or from doing something productive. This won't happen overnight. It will be a gradual process but you'll get through it and you'll be extremely tough afterwards.
Don't listen to people who say that ADHD is bullshit. They don't know what it's like. I had to fight with my parents over this issue, but now I'm better and they've forgiven me. And remember that thoughts, memory, feelings and all that other shit is just chemicals in your brain. Good luck.