The analyses of a text #1

The protagonist is one of royal family members of Amber.
He made a date with Coral, a daughter of the prime minister from a neighboring country Begma.
And he went out with her, showing her the town, and he didn't keep her from going further away by herself.
He came back to the palace by himself.
Her younger sister, Nayda asked him about whereabouts of her sister at table, he answered he didn't know, but he got, in the conversation, an impression that Nayda crushed on him.
He just now visited her quarter to ask her to cover for Coral, as finding her.

"How are you feeling?" I asked.
"Find out," She said softly.
I could not even permit myself a sigh. Duty called. I slipped my arms around her, drew her to me, and kissed her. I held the pose for several seconds, then drew away, smiled again, and said, "You feel fine to me. Listen, there are some things I did not tell you?"
"Shall we sit down?" she said, taking my hand and leading me toward the couch.
Vialle had told me to be diplomatic [Vialle is the queen], so I followed her. Immediately, she continued our embrace and began to add refinements. Damn! And me constrained to rush her out to cover for Coral. If she would, I'd be happy to cover for her afterward. Or any other interesting position Begmans might go in for. I'd better ask quickly, though, I decided. A couple of minutes more and it would be very undiplomatic to begin talking about her sister. Today was just a bad day when it came to timing.
["Sign of Chaos" of The Great Book of Amber by Roger Zelazny]
I'd like to know if "me constrained" means "it had me constrained."
I'd like to know if "If she would" means "If she would help me afterwords."
And I'd like to know if "Or" means "If she wouldn't help me afterwords."
Thank you in advance for your help.