It would take an inordinate amount of hand-waving...
Let's start from the flowers. Can we make a flower develop in a human lung?
And the answer is no, we can't, there's not the necessary space. We can however imagine a flower-analogue that might: some sort of symbiotic/parasitic organism that is usually found on some ground-bound rodent, and grows on its skin. The organism has evolved to avoid the host's immune response and uses it for locomotion, providing some service in exchange - vitamin synthesis, maybe. When it's ready, it releases its pollen to the winds.
Normally the pollen will experience a brief flash of activity upon landing on the host's mucosae or the skin of a pup: it will quickly burrow to a safe place near the skin, and there lie dormant until the appropriate chemical cues will signal it's time to flower. This usually happens when the host is fully mature, in good health and the season is right. The organism flowers slowly and beautifully, sending pollen everywhere and keeping its host healthy to do it as long as possible.
If the host isn't in top shape, that's bad luck for the host and the parasite both. The parasite, as an emergency plan B to ensure its genes' survival, flowers as much as it can, dying in the process and damaging the host, to ensure at least one pollen wave is sent forth.
The pollen might be inhaled by a human being. Normally nothing happens because the chemistry isn't right: the pollen does not exit its dormancy phase, and when it does it dies soon after.
Nobody knows what triggers the disease because even people living next to the flowered rodents do not contract the disease very often. Indeed, most of them never do due to acquired immunity.
The notable exception is when the person is flooded by the right mixture of norepinephrin, endorphin and oxytocins, up to one full year after breathing the pollen (one year being the average time for a rodent to reach maturity). The hormone mixture, which tells a human's organism to start behaving as an unrequited lover's organism is expected to behave, also tells the parasite that conditions are ready to flower. And it happens so long after the pollen exposure, that the relation between cause and effect has escaped the medioeval natural philosophy of your world.
They would rather believe that only refined, cultured city dwellers (those farther from the rodents, and therefore with less immunity - if they knew what immunity was) had the required sensitivity to trigger the heartflower disease, while peasant love is just two animals in rut (this is not so unlike what happened in our own world; most (pre-)Stilnovist poets in the 1200's said as much).
Unfortunately the "flowers" don't agree with human bronchi, so they are quickly torn off and coughed up. The cycle repeats until either the human dies, or the hormone mixture is altered. The new mixture has again to be close enough, and that happens when the love is returned and, better still, consumed.
It is sometimes possible to excise the organism if it's near enough the top of the trachea. Those that have this done to them usually die of complications or infections (medioeval times being what they are). When they don't die, they almost invariably suffer from PTSD and unconsciously avoid the same situation - when they would start feeling in love again, they get flashbacks instead, which quickly kill the mood.
Otherwise, the flowers would continue to grow, and some pollen find its way throughout the circulatory system. This, plus some cases of vegetative endocarditis, led to the mistaken popular belief that flowers grew in the heart as well as in the lungs, whence their name, "heartflowers".
