From Longman Dictionary of Contemporary Englishlovesicklove‧sick /ˈlʌvˌsɪk/ adjective LOVEspending all your time thinking about someone you love, especially someone who does not love you a lovesick teenager
Examples from the Corpus
lovesick• From Honk Kong comes a confusing romance about chance encounters between lovesick cops and unusual women.• In her writing she recounts a story about one lovesick cowboy who brandished a pistol at her.• If you're slim, honest and have a good sense of humour then send your photos to this lovesick laddie.• If only she weren't such a lovesick loon.• He knew he was behaving like a lovesick teenager.• You're acting like a lovesick teenager! 