Can I be charged with OWI when I was home 15 to 20 minutes before the cops showed up?

If you need specific legal advice for your particular circumstances, I encourage you to privately consult with a lawyer. If you are charged with an offense and cannot afford to pay for your own defense, the court may appoint you an attorney payable at the public's expense. You have a right to counsel. You should either retain a lawyer or ask for a court-appointed lawyer at your arraignment. You are presumed innocent. They need to prove your guilt "beyond a reasonable doubt." There may be some issues with their case based on your description; however, much of it will probably hinge on the potential testimony of the person who saw you driving. Ultimately, based on your description, there may be issues with your arrest, your tests, and other measures. However, those are issues for a properly researched and filed motion to suppress as the case proceeds. The prosecutor, depending on what the reports say, probably has a much different version of events based, in part, from the person who called in the incident. As for reading you "your rights," that's only an issue if they wished to question you when you are not in a position to leave, i.e., custodial interrogation or custodial questioning. If they did question you while you were in custody and they did not read you your rights, it may be grounds for a motion to suppress any alleged statements that were made during that questioning. You need counsel and as soon as possible, especially given the stakes regarding your military career.

Sounds like a very tough case for you as the facts are difficult. You need a skilled attorney on board right away to figure out your defenses.

You know that you should be engaging an attorney, now! Speak with no one about the incident until you have counsel. You have possible defenses.