I posted a question...
It got half answered, so I used it to create my own answer. It got down-voted for this, but I don't know how else to do it. Should I edit the other users answer?
I have no idea why you got downvoted and received the comment: "no need to make an answer out of another answer". The other (only) answer is substantially different, and you did make a note to the poster that it only got you on the right track, not all the way.
It's great that you posted your solution, but maybe out of politeness you should accept the other answer.
By the way, I have seen the user who downvoted you be confrontational quite a bit, so I think this is an exception rather than the rule.
Nope, absolutely nothing wrong with this.
Here are my guidelines:
Obviously it's up to you to decide on a case-by-case basis what qualifies as a minor and what qualifies as a substantial edit to the original answer, but it's really not that big of a deal. Posting your own answer to your own question is very much encouraged around here.
Don't worry too much about people voting you down. They could be in a bad mood, they could be using an iPhone where it's almost inevitable that you cast an erroneous downvote, they could dislike your proposed solution, or tons of other possibilities.
You are under no obligation to accept any of the answers to your question. You're just asked to pick the one that was most helpful to you in solving your problem. If you've done some of your own work and expanded on an answer given by another user, it's extremely helpful to post your own complete solution. This is far more likely to help others who arrive later in search of an answer to the same question.
Also see the somewhat-related question (although not exactly, because in this case I think you're actually adding value): May I summarize all answers
If the answer got you on the
right track, that should be your answer!
If the answer did not fulfill your requirements for the question, comment as such and maybe the user would expand their answer to fit what you might need.