Tiz, are you saying you made your own LOR and asked the professor to just sign it? Is this the way it works? I was just going to ask them to write me one and tell them my motivation for joining the Navy. Is there anything I should ask them to put?
When I was a civilian in college, my rule was to ask first via a signed formal letter of request (about 2-3 paragraphs stating my goals, why I felt their opinion of me mattered and of course respectfully asking permission), I got a yes 100% of the time via a face to face talk in their office about the letter, I worked on the LOR over the course of a week and turn it in to them to sign face to face. The process demonstrates your professionalism and validates their opinion of you. You have to
"offer" to write it for them as
it will give them an idea of all you have accomplished they may not be aware of. Be sure to offer that to them, not tell them. You can't be presumptuous, they may very well want to just interview you and write it themselves. That's fine.
In the fleet the process is the same, minus the flattery and fluff. You would just route your award/FITREP through the chain of command through the quickest physical means in a routing folder for approval. It is very routine, complete with written procedures, time frames and a routing matrix.