Is there a non-addictive drug?

Non addictive drug: Yes there are a multitude of non-addictive drugs. In fact the overwhelming number of drugs are non-addictive. Concerning your question, there may be a non-addictive drug for the condition you have and it depends on the condition.

Of course: "drug" is a very generic word. Antibiotics, antihypertensives, anti-diabetes medications are all drugs. Any substance from outside the body that changes our physiology is a drug. Only a handful of drug classes produce tolerance and withdrawal, which is what makes a drug dependency-producing (i don't use the term "addictive" drug - addiction more involves the person, not the medicine).