Sunni's throwing up..

Hello! Thank u all for ur words of encouragement. I am feeling better about the new cat which I have finally decided to call Zebra. The reason I decided on this is because last night, I finally saw the "WHOLE" cat and noticed her black stripes are shaped just like a zebra SERIOUSLY!. Zebra is doing much better- she has been very playful last night, comes out more now and allowed me to pet her for ONE SECOND. She seems very interested in Sunni but Sunni still growls and hisses at her.
I am worried about Sunni though because yesterday morning, she threw up in my bedroom then last night, she threw up again on my bed. I am trying to decide if I should take her to the vet or wait for a couple days to see.. What do u guys think??? One problem is that I don't know any vets here in Maryland so I don't know where to start. I have a list of vets and think today I will start calling around to see who sounds like they will take good care of cats then see if I should make an appointment next week or so to have both cats checked. (Am worried about the cost though cuz I have spent alot of money on both cats this last 2 weeks! )
I will take ur suggestions about the wet towel and rubbing both cats with it so they'd get used to each other. I have not shut either cat up in a room and I prefer not to if possible because I don't want them feeling trapped. So far, they have been giving each other space. Sunni just growls and hisses if Zebra comes too close and Zebra is smart enough not to push her luck with Sunni. :tounge2:
Sunni still bites me
sometimes and still hides under my bed but she is STILL sleeping with me at nites and PURRSSS when I pet her at bedtime so that is helping me hang in there.
I will keep u guys posted on Zebra and Sunni. If u have any suggestions or advice, please feel free to let me know ANYTIME!