First of all, you need to be careful when you use compound adjectives such as "X + -ed", "X + -ful", or "X + -ing", etc. It is very confusing but it has to be understood from the verb usage, i.e. "intransitive"/"transitive" or "active"/"passive".
You doubt about yourself, and you are not doubted about yourself. In this case, "Doubt" is an intransitive verb. However, you doubt someone else or things like ability, value, etc. and it becomes a transitive verb. Therefore, you have to use "self-doubting" which means:
Lacking confidence in oneself and one’s abilities; unconfident:
[Oxford Online Dictionary]
The word comes from "self-doubt" which means:
lack of confidence in one's own motives, ability, etc.
[Random House Kernerman Webster's College Dictionar]