First, before you read my full answer/suggestion below I want to make sure you have taken her to a doctor and made sure there is no physical reason for this - perhaps tongue tied or low muscle tone or a severe allergy. If you have done this, my second suggestion is to contact the school district and have her tested, they will have people help you for free and give her schooling to get her up to level.
Third, take her off the bottle. I followed the picky eater plan (below) with my older daughter. But it wasn't until she was almost 4 that she got an appetite. She always fed herself, that was never an issue, but she had 5 bites and called it quits, saying she was done. When she was almost 4 she still was not sleeping through the night and in desperation I took all milk away as I had read a study that said the majority of preschool sleep problems were really hidden milk allergies.
She did start sleeping through the night, but more importantly, for the FIRST TIME EVER, one week shy of being four years old, my daughter asked for food and said she was hungry. This was after only 4 days of no milk, she was sleeping through the night finally (and it was anywhere from 2 to 20 times a night she was up prior to that) and her hunger mechanism kicked in. It was honestly a miracle when she ate 8 chicken nuggets in one sitting, normally she ate 1 1/2!!
here is my picky eater plan, since you asked the question I am hoping you are at the stage where you are willing to take a risk and change your ways. I have had multiple daycare kids come to me, yes at age 3 even, just like your child, and this works.
There is a great book by William G Wilkoff, MD called Coping with a Picky Eater that every parent or provider of kids should read and have a copy of. http://www.amazon.com/Coping-Picky-Eater-Perplexed-Parent...
This book has what I call the Picky Eater Plan. I have used this plan with kids that literally threw up at the sight of food and within 2 weeks they were eating normal amounts of everything and trying every food.
First you need to get everyone who deals with the child on board. If you are a provider it's ok to make this the rule at your house and not have the parents follow through but you wont' see as good results as what I described up above.
The plan is to limit the quantities of food you give the kid. When I first start with a child I give them literally ONE bite worth of each food I am serving. The book suggests that every time you feed the kids (breakfast, morning snack, lunch, afternoon snack, dinner) you give all 4 food groups. So, for lunch today I would have given the child one tiny piece of strawberry, one spoonful of applesauce, 3 macaroni noodles with cheese on them, and 2 oz of milk. Only after they ate ALL of what was on their plate would you give them anything else. They can have the same amounts for seconds. If they only want more mac and cheese, they only get 3 noodles then they would have to have more of all the other foods in order to get more than that. If they don't eat, fine. If they don't finish, fine. Don't make a big deal out of it, just make them stay at the table until everyone else is done eating. They don't get more food until they are sat at the next meal and they only get what you serve. When I first do this with a child I don't serve sweets at all. So no animal crackers for snack but rather a carrot for snack. Or one of each of those. I don't make it easy for them to gorge on bad foods in other words. Now if they had a meal where they ate great then I might make the snack be a yummy one cause I know they filled up on good foods.
Even at snacks you have to limit quantities of the good stuff or else they will hold out for snack and just eat those snacky foods. I never give a picky eater the reward of a yummy snack unless they had that great lunch prior to it.
It really is that easy.