Hasib, First, GuideDogSaint below is exactly right. The writer was saying they don't reply to these famous sports players, musicians, and actors asking them out because they already have a boyfriend. But this phrase is very non-standard slang, not standard English. In fact, even for slang it's very uncommon slang. I've never heard anyone use it before (and I'm a native English speaker). But the word "up" is used in many phrases which mean "fullness" or "completeness": "Fed up" means "full of frustration or anger to the point where you cannot take any more." "Dressed up" means "dressed in fancy clothes," and implies that you cannot get any fancier. "choked up" means so full of emotion that you cannot speak. Many of these phrases are sometimes accompanied by "all:" "All choked up" or "All dressed up." When you put gas in your car you "fill up." When the car is full of gas you might say it is "all filled up." Therefore, I assume the phrase "loved up," implies that the speaker was "already full of love" so they can't take anymore. This is why, as GuideDogSaint says below, they must already have a boyfriend.

It probably means she already has a boyfriend she is in love with.