I'm not sure what to say that will help. I think your feelings could stem from many different areas. It could be something about your feeling like you have to earn your healing and when you do reiki you haven't "earned" it so you don't "deserve" it. It could be about feeling a loss of control. When you take a walk you feel good and you've "earned" it sure, but you've also made it happen all by your self. For some people being self reliant is really important. Asking for help or admitting that surrending your care to others (in this case the universe) can be a scary idea. It can also create this idea of resentment or feeling that doing so is cheating.
Letting go though is still doing something. Deciding that you need more than youreself to get a healing to work for you isn't cheating, it's just acknowledging that we aren't a one man show. I don't know whether or not this is actually where you're hung up. but getting reiki done whether self reiki or done by others isn't cheating. For some people it takes more work than others to acknowledge that they need healing and they need help, but it's still work. Asking someone else or the universe as a whole for energy is doing something.