alright. as a native english speaker, i'll try to explain what sounds weird to me about "there is only an alternative".
"there is only an alternative" means, to me, that "an alternative" is the only thing that exists in this situation. and the word "alternative", by definition, cannot be the only thing (otherwise it wouldn't be an alternative to anything!).
"there is only one alternative", on the other hand, focuses on the number (one) and indicates that there is one alternative, as opposed to many--a perfectly reasonable concept.
I think that's why "there is only an alternative" sounds wrong because alternative implies more than one, but "an" and "only" implies just one. Whereas "there is only one alternative" suggests a situation where there were 2 or more options but someone has rejected all but 1 option and the other person says "there is only one alternative [to the option(s) you have rejected]"