We got a 10 week old kitten last weekend and after a week of keeping her separate from my current cat, and doing the scent swapping and sniffing under the door, today was the day of the first visual interaction.
The kitten was in a cage borrowed from the vet, and my other cat Gizmo was at the door of the room the kitten was in.
There was a bit of hissing, and the poor kitten was so terrified she was sick and then had diarrheoa. She has been suffering with diarrheoa all week so I feel like I've just made things worse now!

What do I do now???

Poor kitten If he has had the runs since you brought her home it could be a change of food. Give her a bland diet for a few days - plain boiled chicken breast is good with some of the liquid as a broth. if there's no improvement get a vet to check her over. When you register with a vet you usually get a free check up anyway.
As for the introductions keep them apart for a little longer and when you let Gizmo see her be with her stoking her to tell her it's okay. Talk to them both very softly and keep calm yourself. You can expect some hissing and growling to start with but I doubt if her reaction to Gizmo caused the diarrhea.

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How we behave toward cats here below determines our status in heaven. - Robert A. Heinlein
http://www.lambchopsiamese.webs.com

i'd follow this

Integrating Kittens with Cats

slowly - if you think the visual has upset kitty- wait more

I have the opposite problem! I have a 3yr old much loved pampered cat, who has shared her home with daughters 20 week old kitten for a couple of weeks while daughter on holiday. The cat (Kizzi) has started a flicker in her back bone when she eats, she then starts to flick her head to look at twiches, her tail swishes and she then goes loopy running around the downstairs like a crazy mad-thing...whats going on? She is eating well, but wants to get out straight after eating, if she doesn't she starts twitching...taking her to vets tomorrow....so me looking after daughters kitty to save her cattery bill may mean my cat needs expensive vet treatment...I told daughter never again, nothing upsets my cat..!

I kept them separate but Kizzi did see the kitten now and again when she was outside and kitten was in lounge, and obviously she smelt she had been around... kitten was put in a separate room when kizzi came in.

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Kizzi's Mum