You raise a lot of issues that an attorney may be able to take advantage of. You need to contact a solid DUI attorney in the area such as Jeff Meadows or Larry Denny and sit down and go over the facts, the charges, and the defenses you may have.
You should consult an attorney. A challenge may exist in the formation of what Ohio law calls reasonable and articulable suspicion to ask you to submit to field sobriety tests. The NHTSA manual provides insight into what is required to formulate reasonable and articulable suspicion as well as what is used to constitutes probable cause for your arrest. Obviously, any attorney would need to hear more of your story and see the discovery before making a determination. Other issues may exist as to how the "tip" was conveyed to the investigating officers. It is always best to consult with an attorney and tell your full story.
My question is were you on base (military controlled area) or not? If you were off then why is the military police involved as it is a civilian matter. You may need to also discuss with your attorney (court appointed or private) as to if there was even jurisdiction for the MPs to cite you with any offense.
Were you ON the base when this occurred, because your question doesn't make that clear. As far as being arrested, an officer needs to have probable cause to arrest you. Your problem is that you are underage, and since the illegal (per se) limit for blood alcohol for you is 0.02. Since you aren't suppose to be drinking in the first place (unless a parent provided the alcohol), the probable cause standard for you is much lower than it would be for someone 21 or older.
As for the citation for the "refusal", Ohio's DUI/OVI law has a section for those who refuse to submit to a chemical test (blood, breath or urine); HOWEVER, that section (4511.19(A)(2)) requires that you have a prior conviction for OVI. So if you don't have a prior, that charge should get dismissed. It sounds like the officer isn't on top of Ohio OVI laws which may prove to be beneficial in the long run.
There are lots of issues that appear to be present in your fact pattern and I would strongly recommend that you get an attorney invovled immediately. And make sure it is an attorney who focuses on OVI defense.