Is it normal for my kitten to vomit roundworms after deworming?

Hello and welcome to Petco Pet Education Center, formerly Petcoach,
Piggy is very cute, I am sorry she isn't feeling well.

Animals with high burdens (large numbers) of worms can both vomit and poop out the worms and this can be normal. The concerning part of this for Piggy is that she was given a very strong medication to stop vomiting, and is vomiting anyways. This might be a sign that she has such a large number of worms that they might be causing a blockage in her intestines so that they cannot flow through.

I recommend monitoring Piggy very carefully. If she continues to vomit, isn't eating, isn't pooping at all, or if she seems weak, tired, sore or bloated in her abdomen/stomach, then I would get her to a vet right away for x-rays as she might need surgery. Another possible but less likely condition is called an intussusception (where the intestines 'telescope' inside itself and cause death to that part of the intestine) and will cause the same signs as above, and requires surgery to fix. These conditions are unlikely to happen but important to watch for.

If she is otherwise eating and keeping some food down, pooping, playing and acting normally, then just continue to monitor her and you will likely see the worms coming through her poop soon.

Best of luck with Piggy!