back when i was flight instructing, if i was in this situation, i may have been hesitant to declare an emergency, too, cause, i was always under the impression, that's a bad thing to do, that's inviting the feds into my logbooks, the plane's logbooks, the school's books, admitting defeat, etc. however, now, with some perspective on flying in general and the whole industry, hellyeah, declare the emergency, for all the reasons stated above, by others and yourself. good call!
also, don't forget, atc can (and will) declare an emergency FOR you... so, let's say you are landing at a controlled field, and you're pudding on in with one feathered, and try to dance around making the big E statement... if they look out with binoculars and see one shut down, or simply ask you and you say yes.. well, chances are they just might declare the emergency for you. and yes, you, the pilot, still has to fill out the paperwork!
but that aside, good job taking the situation in stride and handling it like a pro.