A "buzz" usually means the feeling of being slightly drunk or high on a drug. "I drank a strong beer and it gave me a buzz", means the person feels a little bit drunk. But a "buzz" can come from other things, like getting a buzz from riding fast on a motorcycle, or jumping out of a plane with a parachute, or kissing someone you're really attracted to.
A "pick me up" also (usually) refers to alcohol. "I feel stressed, I need a little pick me up", means the person needs to have an alcoholic drink to "pick up" his or her mood. But again, it could mean anything that improves your mood. Things like going on a shopping trip, or getting a nice hair cut, or visiting with a friend are all "pick me up" things which improve your mood.