First of all, I understand that it's only a drama and that it's impossible for someone to recover from a heart transplant as well as he did, but I'm left confused because there's really no connection between the heart surgery to his tactile agnosia, because his condition in season 1 has to do with the nervous system/brain stuff. Something like a head injury had to occur between the time after high school and before he moved to Yangyang to be diagnosed with the inability feel anything from touching anything. Unless there's another season to fully explain this, then I'll have to conclude that the writers failed to make a coherent storyline for Woohyuk since his conditions are a really big part of both seasons.

THIS IS JUST ONE OF THE POSSIBILITIES

i searched a few days about both if his medical situation in the drama and i found that another cause of tactile agnosia is because of strokes , also after a heart transplant or surgery exist risk of strokes  , most probably woohyuk had a cerebrovascular stroke and his tactila agnosia is because of that 

 there are some quotes from some articles : 

1. "Follow-Up of the Transplanted Patient

Ischemic stroke is the most prevalent cerebrovascular complication during the follow-up after heart transplantation. After the perioperative period, the only factor that has been significantly associated with an increased risk of cerebrovascular complications is a history of prior stroke, either ischemic or hemorrhagic [5]. No increased risk of cerebrovascular complications was found in patients with atrial fibrillation, anemia, hypotension or hypertension and cardiac pump failure."  https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2994113/

2."Agnosia is usually caused by lesions on the parietal, temporal, or occipital lobes of the brain. These lobes store semantic information and language. Strokes, head trauma, or encephalitis can cause lesions. " 

https://www.healthline.com/health/agnosia#causes

3. https://www.healthline.com/health/stroke#symptoms

During the second season there are signs that something is wrong with woohyuk after the heart transplant , during the running and during the swimming race he lost his conscience