Addiction has both psychological and physical components.
Many sedatives, such as benzodiazepines (e.g. lorazepam or diazepam), do have a potential for both.
Physically, it takes more than one administration to create a chemical dependence, so that is not likely to have happened.
Physically, Nitrous Oxide is not known to create a chemical dependence - I cannot find that in the literature.
However, psychologically, one of the things that many people with substance use disorders say is that they "will do anything to achieve that feeling again." They often think about the pleasure they feel when they are on the drug and have a powerful desire to feel it again. This can be true for both of the above.
Nitrous Oxide IS actually used as a street drug where it's called "Whip-Its" and has harmful side effects. Benzos and other sedatives are sold on the street as well, and also have serious side effects and potentially fatal withdrawal.
If you're worried whether you're physically addicted because they gave it to you once, no.
If you're just thinking "that felt nice," that's not addiction either.
But if you're considering finding a way to achieve that feeling again (via Nitrous Oxide or another chemical), then you're starting the walk down the path to psychological addiction.
Check out these risk factors for being more likely to struggle with an addiction: http://www.mayoclinic.org/diseases-conditions/drug-addiction/basics/risk-factors/con-20020970