What you describe is not psychological addiction. What you describe is physical dependence. The Vicks inhaler contains Levmetamfetamine. It is similar to methamphetamine, but it is a mirror image chemically. It has the same effects on your nose, but it doesn't get you high at all.
What are those effects on your nose? Vasoconstriction. It causes the blood vessels in your mucus membranes to constrict. This reduces the production of mucus, and it can physically open up the passages as well, because the tissues shrink when they are filled with less blood. Two things can happen when you stop the Levmetamfetamine:
1. Whatever condition that was causing congestion is now untreated, so your congestion returns
2. The mucus membranes, having become adapted to that vasoconstriction, flood with blood when the Levmetamfetamine is withdrawn, causing what is called rebound congestion. This can occur as mucus, but you can also have the tissues fill with blood and inflate but stay fairly dry.
Do not switch to a nose spray. That will just continue the same problem.
You need to quit the Levmetamfetamine. Use hot showers to reduce the discomfort. In a day or two everything will be back to normal.
If I am making dependence sound like addiction, that is because dependence is part of addiction, but addiction involves several other elements in addition to dependence.
You'll be fine. You just have to quit cold turkey.