At 12 weeks, their sleeping becomes more like ours. This means you have to gradually teach your child how to fall asleep. The first essential ingredient is getting baby to bed before baby is overtired. Overtired babies will just cry and cry and cry, till exhausted. At that point, they pass out. But because they are overtired, they only sleep a short while. Sleep begets sleep.
Second, it's time to start a real routine. You need to set the stage for sleep, and then follow it consistently so baby knows what to expect. Our simple routine is: turn on noise machine, change diaper/put on sleep sack. Read a book, sing a song, go in crib. While teaching her to sleep, I would nurse to help get her sleepy. I would put her in her crib awake, and just keep on urging till drowsy, putting down, until she fell asleep.
What you haven't tried, it sounds like, is a quiet room. Babies can get over stimulated, so at nap time--and naps develop on a schedule at 3 months- you need to help baby relax by providing a quiet, mellow environment. This will mean lots of hours in a dark room singing, rocking baby. After a week, baby should be able to put baby to sleep with little help. It's a rough few weeks, but if you hang in there and don't start any bad habits, baby should learn how to self-sooth with very little crying. Pm me for more information if you want. It takes me 1-2week at this age to get my babies self-soothing. Now is when I introduce a transitional object too.
But really,what's going on is that your baby doesn't sleep out of necessity anymore. Newborns sleep when they need to, thus the phrase sleeping like a baby. At 12 weeks, their rhythms become like ours, so after a sleep cycle, they wake up --we do too every night, we just roll over and continue sleeping.
The first thing you should do is get a schedule doing. Wake baby at the same time every morning, and put down for a nap an hour and 15 minutes later, at the longest. This will help jump start a good routine.
I have to go now, but there is nothing wrong. You have an overtired baby that is asking to be helped to learn how to self-sooth.