I know there are a lot of posts like these but I haven’t seen one with my situation yet. I have 3.4 GPA (after first semester of junior year) and i got a 30 on the ACT. I’m going to retake the ACT to try to score higher but I know my GPA is low. I struggle with a mental illness and I missed my entire sophomore year. This past semester is what messed me up because I was (and still am) struggling with my illness and have trouble keeping up with school. I’m very close with my counselor and know she can write me a great letter of rec explaining everything but will it be enough?
Also I’m in state and have a few extracurriculars
It is not likely. What makes you think that you could handle the workload at UM if you already have trouble keeping up in HS? If your illness was under control that might be different. You may end up hurting yourself more with stress. Only 2.7% of freshman had GPAs in your range, and many of those had significant hooks (athletes, etc.)
It is under control. I am doing online school for the semester and will transfer back to my normal high school for senior year. What I meant by still am struggling is that my mental illness will never really go away but I have learned to manage it so I can be productive. I have all As so far this semester and am planning on taking more APs next year. Also about hooks, I do music lessons and theatre in school (not sure if that would help but I have ECs). So my main question is would they overlook the GPA if I said I have an illness plus I show significant improvement in my grades?
Considering GPA is the most important factor of determining admission for UMich, I would say it is not likely. Unless you had a beyond stellar ACT to make up for it, there aren’t many things that will get admissions to look past such a low GPA.
A possible path would be you would have to continue with all 'A’s in your classes with several AP level ones, apply EA, get deferred, keep the ‘A’ grades and AP classes in 1st semester senior, and end up with a GPA around 3.75. You’d have to get your ACT to the 34-36 range too. So there is a path, but it will not be easy.
If you are extremely musically talented, you should apply to SMTD, and a good audition will partly compensate for the GPA. You could dual-enroll in a different school if you wanted to do a different major.
I’m very against this type of mentality because I don’t believe anyone with any kind of disability or mental illnesses should give up on achieving their dreams after their illnesses take a toll on them, but I want you to know for your own sake that Michigan will not help with your mental illness.
It’s a challenge everyday. Between your assignments, quizzes, tests, ECs, thinking about your future (yes, you will be thinking about your future the entire time), trying to make friends, and deciding your major, you won’t be in the best mental health position. It’s tiring and stressful. You’ll feel inadequate. You’ll go for counseling and it’s help, but at the end of the day, they can only do so much.
I don’t say the above to discourage you or scare you. I just need you to make sure Michigan is the environment you want to be in. If it is, you’ll love it as I love it.
Now for the technical part, you will need all As from now on and at least a 34 ACT to be competitive enough. I assume your LoRs will be good from what you’ve said, and your ECs are good (not hooks, but good). Make sure your essays are spectacular and BE YOU. They can see right through a fake essay. Explain your struggle with mental illness if you’re comfortable with that somewhere on the application, but don’t make it an excuse; you want to come off as someone who can overcome. Apply as early as possible.
I will say to ignore anyone who tells you to not apply if you can pull a 3.6+* and a 34 ACT. You never know. But don’t get your hopes up, again for your own mental health.
*My friend got in with a 26 ACT and 4.0 GPA. I got in with a 32 and a 3.93. I’m assuming, maybe incorrectly, that a 3.6 and a 34 would “balance” to a competitive level. I wasn’t the best applicant as you can tell, but I’m now a freshman here 
Give it a go argents. If you can raise your GPA (over 3.7 this semester and the first semester of senior year, improve on the ACT (to say a 32), and write excellent essays, you certainly have a shot.
But please, remember that Michigan is very intense academically. If you enjoy a good challenge, go for it, but if you prefer a more laid back experience, there are equally good schools that are less intense, and perhaps those would be better suited for you.