But O heart! heart! heart! (5)
The speaker does a literary double-dip here. He uses the heart in both an apostrophe and a synecdoche to communicate the emotional bonds he feels for the captain.
Here Captain! dear father! (13)
The words “dear father” communicate a positive emotional bond with the captain (as opposed to "I hate you, Dad!"). The captain is a positive father-figure and we see male-bonding at its most successful.
This arm beneath your head; (14)
The intimacy of nursing isn’t thought of as masculine in our current culture, but in Whitman’s culture, almost all nurses were in fact men. For real. You can read Whitman’s about emotional bonds with wounded and dying soldiers in his Memoranda During the War.