You should smell it when you rub or bruise it, so nothing seems to be wrong with your plant. When it was in the bag and it smelled when you open it, it was probably rubbed by the bag.
There was recently a similar question answered by Bamboo, where the OP asked the same for lavender.
Here's what they look like to me:
Holy basil or mint
I want to say mint, but it looks a bit different. Not sure.
Marjoram, or possibly oregano; if it is a basil, then probably Spicy Globe Bush
Some mint-like plants may be other things, such as pennyroyal or horse mint.