Is Hyoscyamine sulfate sublingual a narcotic?

No, it is an "anticholinergic", meaning it "slows things down" and is used for bowel issues like IBS, CROHNS, etc. The main side effects are urinary retention, dry mouth, dry eyes, and constipation (or treatment of diarrhea on how you look at it LOL).

No, hyoscyamine is not a narcotic but you could put it in the safe because taking too much of any medicine may be abuse.

Hyoscyamine produces many effects in the body, including relief from muscle spasms.
It also reduces the fluid secretions of many organs and glands in the body, such as the stomach, pancreas, lungs, saliva glands, sweat glands, and nasal passages.

Hyoscyamine is used to treat many different stomach and intestinal disorders, including peptic ulcer and irritable bowel syndrome. It is also used to control muscle spasms in the bladder, kidneys, or digestive tract, and to reduce stomach acid. Hyoscyamine is sometimes used to reduce tremors and rigid muscles in people with symptoms of Parkinson's disease.

Hyoscyamine is also used as a drying agent to control excessive salivation, runny nose, or excessive sweating.

https://www.drugs.com/mtm/hyoscyamine.html