Sounds like a wonderful dream! On this forum, we often examine the people in our dreams as an aspect of ourselves. If you apply this here, it seems you have united with your opposite (male) aspect and all that entails for extreme unction. Quite spiritual sounding, actually. To me, explains the heightened ecstasy, peace and love. You join ultimately with yourself, you are whole as one, as you say.
Have you happened to make a committment to your self - self improvement, self-care, etc? Either way, it seems this is what you are giving yourself in the dream: self-love. And you accept it, obviously.
To me, the rings symbolize the intention for this to be a lasting committment to this union and merging of whole self. Maybe at this point you are still 'courting' this relationship with yourself but you really desire this to be a life-long committment.