Cloud-based medical data indexing enhances clinical data retrieval, but raises concerns about the privacy of medical data and the patterns of their searches when subjected to new quantum attacks. The privacy-preserving indexing framework proposed in this work is a hybrid between post-quantum key derivation, cryptographic hashing, probabilistic security and encrypted keyword vectors. Medical documents are converted to vector format, and queried with trapdoors, which are random but contain specific keywords and access patterns. Lattice resistant primitives provide security against classical and quantum adversaries for construction of indexes, processing of queries and establishment of session keys. Experimental testing shows that 96.8% retrieval accuracy, 34.6% lower search latency and 29.4% communication overhead reduction are achieved compared to the conventional encrypted indexing. It provides privacy, allows for searches that are not connected to the other data, and enables quick retrieval of data, thus helping secure cloud-based healthcare applications without compromising patient privacy in the post-quantum era.