Wanting to keep someone wholly to yourself is read as insecurity dressed as love. The dream asks what you fear would happen if you loosened your hold.
Has this come up in your dreams before? What was going on in your life then?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.