Public displays of affection😳

Chloe • Snapchat - chlobrap
On nights out my SO becomes reeaaally affectionate and wants to kiss loads and stuff and I find it really awkward to do that in front of people. I don't like to make people feel uncomfortable or like they're third wheeling. This makes him really upset and he feels unwanted. We argue about t every time we go out drinking. I'm trying to show him affection but it's not enough. How do I stop him from taking it so personally? He just doesn't seem to understand why I care about what people think. Any advice at this point would be helpful, we're going in circles right now!