Heraldic matters in many countries are watched over & are continued by bodies of Heralds. They are usually associated with a monarchy or an imperial nation.

A heralds duty can include: creating arms, genealogical research, drawing the arms for a person, identifying arms and more.

The most famous heraldic authority is that of the College of Arms in London. Other countries may or may not have heraldic traditions.

Remember, not all countries have family coat of arms for a particular surname. Keep this in mind only a few countries actually have "Family Arms for a Surname"

Armorial bearings (arms) should be considered legal property of the owners and not used by anyone not authorized to do so by the owner.

As to shops with arms in it for t-shirts, plaques, posters, etc., please consider these to be novelty items.  Well-meaning people sell these and many may not realize the true nature of the usage of arms.  However, many of them also have databases available for them to search.  Use these services if you want - and use the results for jump off points in your own research.

Check the persons country of origins page on the wiki for organizations, authorities & specialty sources for more heraldic information.