Are all forms of Dukkha related to a sense of self?

A few days ago I started reading books about Paticcasamuppada because I realized how little and shallow was my understanding on this capital matter. Despite getting the gist of it, I still have problems understanding the exact details. For instance, I understand that dukkha arises from the 3 kinds of craving (kama, bhava, vibhava), and that craving is the condition for the arising of sustenance/clinging/fuel. I've been reading a book based on Dhamma Talks given by Buddhadasa Bhikkhu (Under the Bodhi Tree) on the topic of Dependent Co-arising. There it is said that all kinds of suffering are born from clinging to "I" and "mine". Is that always the case? If attachment and obsession is developed towards some kind of feeling, is always the idea of a self involved in that process? Couldn't be the case of some obsession to, for example, a pleasent feeling without thinking about it as "mine" or "me"? Couldn't we just attached to a past feeling on itself? Or to put it in other words... Is the arising of the idea/perception of self always necessary for the arising of dukkha? I'm not sure if I'm expressing my doubts correctly. Thanks in advance for your time and patience.