Please be patient when it comes to answers as we just recovered from a crash and there is much to do to get the board going again. Instant answers aren't always the best ones to receive in a situation like this
What you have is common when you introduce two cats together. There will be hissing, posturing, swatting, growling, chasing as the two try and figure out just how to share their space with each other.www.catsplay.com
If you don't have a cat condo, I would suggest you purchase a nice sturdy one. Cat ramps and cat shelves are good too. www.katwallks.com
You want to create an illusion of space when there is none (to speak of) A cat needs to feel secure, and sometimes getting off the floor is all it takes to settle things down a bit.
Also, when they did meet, if you carried the newcomer into the room, you automatically created tension between the two cats. The higher the cat appears the more in control of the situation it is. Alpha cats are always high cat on the totem pole, and will seek out the tops of dressers, counters, shelves in a multiple cat household. So if they do meet, let them meet casually, on their own terms. Keep your door cracked between the rooms, keep your stress level well down. If they sense you are upset, as your post indicates, you will transfer that stress right to them.
If they hiss, don't yell or try to get them apart. Leave them alone but watch them causually. Your warning signs that there will be a war are:
narrow slitted eyes and predatory stare
tail tucked low between the legs, almost not visible
ears flat back
If they tangle, keep a dark blanket that is fairly heavy nearby and when they roll and rabbit kick, throw the blanket over them gently. It will startle them apart.
Stay away from your cats for a few days as far as petting goes, you are liable to get bit while so many new scents are in the house. You can alleviate some of the scent stress by one of these methods:
use vanilla extract several times a day, small amounts, on their chins, and the base of their tails
dust each cat with brewers yeast several times a day. If your cats do not get aggressive on catnip, you can put down some loose leaf catnip and some brewers yeast and mix it up. The cats will come over and play and roll, and their scents will combine with the catnip on their fur and they will smell the "same."www.biovet.com
has a product called a Feliway Comfort Zone Room Diffuser. Invest in two of these and start burning them in the two rooms where the cats most likely converge~
Good luck! And really, it doesn't sound to terrible, they will sort it out in time-