Cheating

Hello, my name is Luna. Last week, I remembered at the last minute that I have a social studies assignment due the next day. This homework required a lot of research, so I was not sure that I had the time to finish it. I called my friend Judy and asked if she could show me her homework. I did not intend to copy her homework, but I could not come up with an idea and I did not have time to do the research. Eventually, I changed my assignment a little based on her assignment. I thought this would not be a big deal. The teacher scored our assignments and returned them a week later. But my score was higher than Judy's. Judy was upset when she saw my assignment and my higher score.
It is cheating to copy someone else's idea as it is, but I changed it a little. Is this still considered cheating? Should I tell Judy the truth and apologize?