Sure. Once I was at a party. I saw this guy across the room and thought he was my old friend. So I went up to him, put my hand on his shoulder and said 'Hey, long time no see!'. But he just gave me a strange look and said he had no idea who I was. I was so embarrassed and tried to laugh it off, but it was really awkward.
Awkward pauses can also make a story long and awkward. Say in a conversation, there are long silences because the people don't know what to say next. This can stretch out the story and make it feel really uncomfortable. Also, when someone does something completely out of place in a social setting, like accidentally spilling a drink all over someone important at a formal event, it can create a long and awkward scenario. There will be reactions, apologies, and attempts to fix the situation that all add to the length and awkwardness.
Well, one awkward Valentine's Day story I have is when I planned a really elaborate dinner for my partner at a fancy restaurant. But when we got there, I realized I had left my wallet at home. It was so embarrassing having to explain to the waiter and my partner. Thankfully, my partner was understanding and paid, but it still made the whole evening feel a bit off.
I heard about a guy who ordered a huge teddy bear for his girlfriend for Valentine's Day. When it arrived, it was so big that he couldn't fit it through the door of her apartment. He tried every angle and finally had to take it apart outside just to get it in. His girlfriend was laughing so hard at his struggle that it made the whole situation really awkward but also really funny.
One common element is hesitation. The characters often hesitate to make a move or say how they really feel. Another is clumsiness, like physically tripping over in front of the person they like.
A totally awkward love story might involve one person being too shy to make a move, while the other is clueless. They keep missing opportunities and end up in comical and cringe-worthy situations.