Need some dental expertise! my teeth feel loose after a deep clean at the dentist, is this normal?

Not unusual: Deep cleaning often needed in presence of gum disease, pockets, bone and gum loss. The services of a periodontist, a gum/bone specialist may be in order.

Deep clean: Deep cleaning is also called scaling and root planing and is necessary to treat periodontal disease and clean plaque, tartar and debris from the coronal (part of tooth you can see) and subgingival (part of tooth root under gum). If there was a lost of debris it can form a "splint" tieing teeth together, remove it and it can result in the teeth feeling loose or mobile depending on severity.

Scaling/Root Planing: Two scenarios here: First, it's usually more soreness of the tissues surrounding the teeth that make a patient feel like the teeth are loose & which will generally subside in a few days. Also, even normal healthy teeth have some minor tooth movement. Or... your teeth are somewhat loose from periodontal (gum) disease which hopefully will improve with cleaning & proper oral hygiene. Ask your dentist

Periodontitis : It is common, it should tighten with time when periodontal health improves. The fact that deep cleaning was recommended signifies a presence of bone loss. Scaling &root planing is the first standard treatment for periodontal disease that removes deposits, decreases gum inflammation. Swollen gums often misrepresent presence of mobility and often patients thing all is OK but disease is there.