Henry kissed Tom, which made things awkward between them. Tom then enlisted to put some distance between them. Not sure if Tom developed feelings for Henry or not -- this is very ambiguous. After a terrible battle, Tom was heavily traumatized. Henry visited Tom, and Tom snapped at him because he blamed Henry for his predicament.
Tom later on regretted his actions, and he was worried that he would actually kill Henry the next time he visited, so he took his own life. Tom was suffering too much to live on anyway.
I need to restate something - Janet said that Tom enlisted out of war romanticism, and not because of Henry, but this isn't confirmed, since it seemed from Tom's words that he did actually enlist because of Henry.
Tom is just traumatized. He is in an unstable condition. I don't think it's anyone's fault. Tom wasn't really "always glued" to him either. They shared their bromance moments. Tom treated Henry as a good friend, but Henry always loved Tom and crossed the line. To be honest, Henry kissing Tom despite knowing he already had a fiancee who was also his friend was a dick move. Dick move as it is, he shouldn't be to blame for Tom's PTSD. Tom then ran away and told Janet about it. Not long after, he enlisted.
Wait, what just happened? Why he killed himself? I am totally confused...