I would suggest that you go to www.nogreaterjoy.com and read as many articles as you have time for in their archives. I have been reading them and have learned some interesting things about children. For instance, babies can be trained and conditioned. This is not punishment, anymore than teaching a puppy not to pee in the house is punishment. However, since a baby has about the intelligence level of a puppy, you can condition it by training.
When a baby is only a few days old, if she cries, she has a need that needs to be dealt with. However, by the time they are about 4 or 5 months, they suddenly discover that they can cry for for wants, too, and that their parents don't know the difference. For example, my 8-month-old will cry if I take a toy away from her. I didn't hurt her, I didn't deprive her of any of the necessities of life, and her diaper is clean and dry, and her tummy is full, but she cried anyway. She wanted the toy. She didn't NEED it, but she wanted it.
So your little one doesn't want to go to sleep. She wants to play with the family. She could be teething--so try some gel or something and see if that works. If it doesn't, then she's just being ornery and spoiled. And because eventually you pick her up, she has learned to persist. She is also old enough to understand you. Sometimes I put my baby down for a nap and she protests (even though I know she is tired, because 2 minutes ago she was rubbing her eyes and looking sleepy). She tries to sit up. I gently force her back into a laying position and tell her to go to sleep. This makes her cry harder, but by now she has learned that it is pointless to try again, because she will not win. So she cries for a few minutes and then goes to sleep. This does not happen every time, but sometimes it does (like today). You will have to be consistent and make her crying counter-productive. If you believe in spanking, try giving her a gentle swat with something that will sting a little (NOT your hand--hands should be for nurturing and anyhow, if you hit a baby with a hand hard enough to hurt, you could do internal damage). I use a chopstick or a 12" flexible twig. Put her down, tell her to sleep, and then let her cry for a bit. If she doesn't start calming down, come in, but don't pick her up. Give her a little swat with the switch on her legs (it should just sting a bit but not damage the skin--test it on yourself first) and say firmly, "I'm not going to pick you up. Stop crying and go to sleep." At first she will cry louder because she has suddenly been deprived of her "rights" to rule, but don't give in. She keeps doing it because she is winning. If you don't let her win, she'll eventually get the idea. She may fall asleep from exhaustion the first night, but the next night if you won and she didn't, it will be easier.
About raising her voice, I really don't know how I would deal with that. My little one doesn't do that, and 3 months is a lot of difference as far as vocal development is concerned. See if you can see why she's doing it. If she seems to be doing it to get attention, try making it counter-productive (only responding when she speaks softly). If you are able to get her to stop, do whatever it is you do, and be consistent. It's like a cat that is trying to get in the house. If you consistently deny them the privilege of entering, they will soon cease to try. However, if you let them in sometimes, they will always try, even if they get literally kicked out 95% of the time--the 5% that they win makes it worth it. Babies and toddlers are the same way. 100% consistency will make for more obedient, and, believe it or not, happier children.
Hope that helps. Let us know what happened.