A shopping bag is read as what you are bringing home from the wider world: new ideas, needs, purchases of the heart. A torn or overflowing one hints at taking on more than you can hold.
When this appeared in your dream, what were you feeling?
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.