I would like to attend Ohio State University because it has been a dream of mine as well as a planned commitment that I have been waiting for all my life.
You can impress them with your grammar if you do this:
I would like to attend Ohio State University because it has been a dream of mine as well as a planned commitment for which I have been waiting all my life.----- this is not necessary, though! The way you wrote it was okay, and only staunch grammarians would complain about it... :-)
I have a passion for the Ohio State football team; I am in awe of the amazing program Ohio State has developed. --- I don't want to read about these things yet.. not in the second sentence. It is better to give an intro that tells the main ideas your essay will cover. Then dedicate a para to talking about football, a para talking about your mom, a para talking about your academic interests, and so forth.
One para = one idea.
Really, though, I think it might be best to only mention football and your mom's experience briefly, and concentrate on writing about why this school will be best for your particular interests in medicine... tell about the philosophy of the school and your philosophy of medicine, and how they are related. That would be cool!!