There are a couple of observations that can be made in the order of depth:
The speaker could hear the blood flowing in his veins.
In order to hear one's bloodflow, you either need a stethoscope or a VERY quiet environment. This implies they were together alone in a silent room.
Even in a fairly quiet environment, it is unlikely that one would be able to hear the blood flowing through someone's arm. Pulse can be heard, but the blood flow itself is not something you hear without concentrating. It is quite likely that the speaker was not distracted, and had their undivided attention on the other person.
You don't put someone's hand on your ear just like that. The situation seems to be quite emotional.
More quotes would be required to understand the full context.