"Here is a solution to a problem which I could probably have never ever thought of by myself". Now you have a clever solution you can use as a tool in your belt of tricks. You might end up applying to a problem of your own on your own volition. That would be a feat on its own.
How much time did you allocate to working at the problem before looking at the solution? What do you want to get out of SICP? A book won't help you become a master on any subject by itself. Many people slave for tens, hundreds, thousands of hours on subjects that interest them occasionally without what you might consider "progress".
It appears that you did give up and peeked at the solution. So logically, you do not know whether you would figure it out on your own or not - you've lost that opportunity. The thing is, everyone experiences setbacks, pitfalls, speedbumps - FAILURES. This is nothing to be ashamed of and if you let it, by learning from it, you can help prevent anxiety and move on.