2 days is very early days - give it at least a couple of weeks before you see improvement. As I regualarily say on here - my parents had 2 that fought like mad for 6 months
!!!! ANd are now best buddies. And when I say fought I mean fur flying, teeth and blood.
Try a feliway diffuser too.
EDIT: copied form a previous post of mine
Give it time and patience - it will get there. These things always take time, at least a few days and the rescue should have told you that! Cats that just get on with a new stranger coming into their territory are very very few and very very weird!
Try scent transferal (i'm going to copy and paste now from another thread I answered, so forgive me . .
'I would invest in a feliway diffuser and set that going (it takes a few days to begin to work) it releases happy pheromones into the atmosphere and chills cats out, also try Bachs rescue remedy in their water. Then start scent sharing, rub all the cats with a towel - under their chins, base of the tail, thier pads and rub this scent all over the house, on the walls, on the furniture etc, overlay the scents so they can all smell each other. Do this again but transfer the scent on to the other cats so they smell of each other, swap blankets over so they effectively sleep on each others scent. Then gradually supervise introductions - there is a good page on this website Welcome to the UKRCC too long to type out again but really worth a read about introducing cats to each other. Keep all this going for a while and they should eventually settle, also show your (gentle) disapproval of any aggression so it isn't acceptable in the house '
I'd walk away when Lilly hisses and growls, with a short 'stop it silly' or 'shht'. Once she is quiet come back. Bad behaviour equals no attention. Also I'd make sure that it is Lilly who is introduced into the house as Milly was there first - so keep Lilly in the smaller area and allow Millie to roam around. If this can be done where Lilly can see that Millie is the priviledged one she will assume she is the alpha female and should act accordingly.
My mum and dad once rescued a cat and the fights that ensued where horrific (mum and dad didn't introduce properly)! It took 6 months but they eventually got there and now are inseparable - so it will get better.
EDIT: Remember poor Lilly has probably been through the mill a bit - she been in a rescue centre, been spayed, now is in a new house - she will be scared (not sure if you are going to move her on again) and nervous. She has been kept in a small room for a while and now has a whole house to explore - scary! I'd keep her confined to just the conservatory for a while - keep her out of your bedroom as that is a place for high status cats and could put Millie's nose out of joint. Give her time to settle in herself. The calmer you are the calmer she will be too - if you worry at every hiss she will feel it and hiss more because she won't feel safe - your tension tells her there is something to worry about. Try to get a routine going. It will happen - and soon you will wonder why you were worried.
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