There's no convenient way, on your own and without a ♦, to see your history of edit suggestions short of keeping track of them yourself. Diamonds possess a limitted ability to view the history of edit suggestions of users, so you might be able to ask one to help you.
As a normal user, you can hackshod your way into finding out, though, by first finding any of your edit suggestions (approved or rejected), and checking the edit suggestion page. At the bottom will be a list of "recent edits", which will shuffle based on what edit suggestion you're looking at. The length of time this will take to sift through depends on your volume of suggestions, but I've successfully used it to review 30 of my edit suggestions once, so it should be able to find your rejections if you keep at it.