If you're sick stay home. It doesn't matter "how sick" you are, you're just as contagious being "a little sick" as being "really sick". If one goes to work like that he's/she's compromising not only his/her own health but all the other ones too. It's not a matter of personal productivity, it's a matter of public heath. If you're company/boss/manager says otherwise they're just being plain irresponsible. If you need a doctor's note, then get one. Not only does it make it official and helps you get out of trouble, but if something gets serious it can help you detect and deal with it.