Apparently it comes from the Japanese words "hana" and "hakimasu", hana means flower, and hakimasu means to throw up.
Hanahaki disease is a fictional disease where the victim of unrequited or one-sided love begins to coughs up or vomit petals and flowers of a flowering plant growing in there lungs
Which will eventually grow large enough to render breathing, and sometimes makes it impossible to breath until the victim reciprocates their feelings