You go to see a touring provider you have a 90-minute GFE appointment with. As soon as you arrive at her hotel room and she lets you in she goes to the bathroom and you hear her throwing up.

Of course you make sure she is ok before you leave as that is just the human thing to do. That is a given. At that point I would ask to reschedule. I seriously doubt any professional SW would object to that request under those circumstances. If she did object, I would offer her something far from the total fee, maybe 25%, as to not get into an altercation with her in the hope that would end the standoff but I would never reschedule with her.

is morning sickness. If it’s morning.

as the door closes, I would help her finish up quickly by gagging her with my dick and then handing her the mouthwash.  Then I would take a shower before I leave.  Why ruin a session I was looking forward to for a little inconvenience like that?

and hold her hair back!

A version of that happened to me once. She was choking because she really wanted to prove to herself she could take the whole thing. So she excused herself, went to the bathroom and threw up. Then she came back and actually DID take the whole thing.

why waste the opportunity.

A variation of option A.  I'd ask if she's okay and what's up with that.  Depending on an acceptable answer I'd stay.  

I would continue with the appointment. As long as she smells and looks decent coming out of the bathroom, there should be no problem.

I'd probably give her a chance to explain what was going on before deciding whether to terminate the date. I'd also check to make sure she was okay, whether I decided to leave or not.

I would def make sure that she is all right. Details would affect what comes next (leave, stay, ...).
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It hasn't come up yet, but is there a chance that this hostess is bulemic?
http://en.wikipedia.org/wiki/Bulimia_nervosa
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Maybe she was sick with food poisoning or a GI infection, maybe you're so ugly you made her puke, ... or maybe it is her condition to deliberately purge. Was this hostess particularly thin or skinny (but that is not always a sign of bulimia)?

Backflushing her throat would relax the muscles a little.  

Something similar happened to me once.  I had made arrangements to see a provider while I was near her town visiting family.  She made no mention of being ill, but when I showed up to her place and although she was dressed in lingerie and heels, I could tell she was under the weather.  Before I knew it, she blew chunks on the floor prior to making it to the bathroom.  Needless to say, there wasn't going to be a session that night.  Before I departed I made a run to the store and got her some pepto bismol and a few other items for nausea, upset stomach, etc. then went about my way.  We ended up linking up a few months after and she was very appreciative that I at the least made sure she was good before I left.  

B.   BUT Id probably leave a little something for her setting up the meet

If it’s just cuz of alcohol.. I don’t see why you wouldn’t still stay. She’ll brush her teeth and use Listerine and you’re good to go haha.

It has never happened to me.  However if it does happen to you, you might go to the mirror to see if you were the cause.

I am thinking if I just threw up, which I havent done since 1974 lol, the lasting I would want is play time. More like bed time, by myself, with a cool wash cloth on my head. lol.  
Btw, your new pics (or maybe just pics I haven't seen before) are beautiful!

Definitely B.