I didn't finish sections of the ACT; what are my chances of making a good score?

I took the ACT yesterday, but on each section I had about 10 questions left. I randomly filled in the remaining bubbles when the 5 minute warning was called then went back to answer what I could. I’m usually good at writing, so my essay might have been fine; however, I am worried that those 10 questions might have hurt me. I know that wrong questions don’t hurt you, but I’m still worried it will affect my scores.
The ACT, I feel, is my only great option to help me get into the school that I want: University of Michigan. I didn’t do so well on the SAT; moreover, it was no where near Michigan’s average SAT scores. However, I am taking it again in June.
Also, if I do not get as great as a score as I hoped, what are my chances of getting into Michigan? I have a wonderful GPA (3.95 un-weighted) and a good rank (top 4%). I actively participate in debate–I’m a captain–and National Honor Society. In addition, I volunteer at a near-by hospital. Given my experience and (possible) poor scores, are my chances slim? At Michigan, I have the option to send either my SAT or ACT scores. (So, hopefully, I did well on the ACT) I understand that scores are very important. I guess I’m a great standardized test taker, or I didn’t study as much.
Thank you for you time; I appreciate it!

I’m not* a great standardized test taker

If you got 10 questions wrong, your score is 26 or 27 at most. Probably less assuming you got some wrong on the remaining questions as well.

Your stats certainly appear to qualify you for Michigan so it’d be a shame if your test scores took you out of your dream school. While test scores aren’t everything, you need to do as many practice tests as you can get ahold of until you get your timing under control. One popular method is to set the timer to 5 minutes less than the normal time for each section to teach yourself to work and process more quickly. If you have a 3.95 GPA and top 4% rank, I’m sure you have the knowledge for a 30+, you just need to get the method down.