Many traditions give the left hand the receiving, intuitive side of a person. Noticing it in a dream is read as attention turning to what you take in, feel or keep unspoken.
Does the traditional reading fit your dream, or did it mean something else to you?
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.