I've been thinking about this recently because I and my roommate (respectively) are currently behaving as personifications of these two adjectives. My girlfriend and I have been dating for about two and a half weeks, which is just long enough to know you love each other, but not long enough to be used to it yet. We're kind of embarrassing, really. When you're lovesick, though, you don't really care about anything that's going on around you unless what's going on involves your significant other. That being said, I do feel a little guilty being so twitterpated while my roommate (hereafter referred to as "Heartsick") languishes in the lugubrious despondence of heartsickness.
Heartsick's story is both endearing and tragic. One of his close friends introduced him to her boyfriend's sister, a gorgeous blonde with a captivating smile the size of Alaska. He was shy, but frankly quite attractive, so he finally gathered the courage to ask her to a relaxing evening at our abode (I say "abode" because it sounds much more romantic than "moderately messy apartment with tacky wood paneling"). It wasn't long before they exchanged phone numbers, arranged future rendezvous, and—c'est l'amour!—became friends on Facebook. We knew it was meant to be when they played Wii Sports. She was doing quite well, unlike Heartsick, who had been pretty boastful earlier but was now pulling some amazing blunders. In a moment of weakness, She made a bit of a stnank and blurted out, "Oh no! I pulled a Heartsick!" (She actually used the name of my roommate, but his name has been changed to protect the innocent... and me.)
Days passed, and both of our relationships flourished—both Heartsick and I held hands with our ladies of interest and celebrated the first kiss of the respective relationships (and bought the corresponding M&M's and ice cream, of course)—but suddenly, like a cobra made out of lightning, disaster struck. First She says that She and Heartsick are taking things too quickly. Then She stops responding to his texts and answering her phone. Heartsick is left in a state of utter confusion, hoping for a clear sign, while She continues to drag him along like that action figure at the beginning of Napoleon Dynamite. Finally, after years (and by "years" I mean "about a week") of vacillating between obsession over She and complete disgust at her behavior, Heartsick discovers that She has left him because of her ex-fiancée.
That, my friends, is another story in and of itself. Suffice it to say that She had dated Some Guy for one month before he popped the question on her, then She broke it off because it didn't feel right. Apparently, what She failed to tell us is that it didn't feel right because She was madly in love with Some Guy. I dunno; you try to figure it out, because I don't get it.
So Lovesick and Heartsick: almost identical words, completely opposite meanings. I think someone went and screwed with the English language, but maybe that's just me. Don't even get me started on the word "cleave."