Should my boyfriend and I make our relationship public or keep it private?

We have been going out for 3 weeks now, and nobody knows about it but the two of us.My boyfriend wants to keep it secret, because he is afraid of drama (rumors, gossip, his past gfs might hate me). I'm fine with being private... sort of. There is two problems with being private. The first being i can't tell/talk to anyone about it. I had my first kiss last week, but i couldn't tell anyone because our relationship is a secret. The second is that because it's private, we have 0 pda. Yet, whenever i see him, i have the urge to hug and kiss him. So to resist this urge, i tend to act like a complete stranger around him. We hardly ever talk in school anymore because of this. So should we make it public and face the unforeseen consequences, or keep it private and have 0 pda and continue to act like strangers in school?