Give Me Novacaine song meaning

Most songs on American Idiot have at least 2 meanings - one is the song's significance in the story line, and the other one is some message that the author expresses through the words of the song.

So, as a part of the plot Give Me Novacaine is describing the insecurity and fear that Jesus of Suburbia is experiencing when he enters his new life. He's tired of being weak, and so he fully surrenders to his alter ego, St. Jimmy. Now he's doing what Jimmy tells him to.

If you look at this song apart from the album, it has a meaning of its own. In simple words it's about feeling shitty and not wanting to feel shitty. When the weight of emotional baggage is bringing you down and natural intelligence makes you realize things you might not really want to know that give you a "bitter sweet migraine" - you can't take it anymore and just want to numb yourself and make the pain go away. Basically, Novacaine is not an intoxicant, it's more of a pain-killer. So, the song is not as much about experiments with drugs, as just about the desire to get rid of the pain.