How can I get my baby to sleep in her crib?
If she has reflux, she shouldn't be lying flat. She should still be somewhat reclined. She knows the motion and the feeling of the swing, a crib feels totally different. Personally, I would convert the crib to a side-sleeper with the head slightly reclined, and at least she'll have comfort close by. She is much too young for crying it out. Even proponents of the concept are very clear that six months is the bare minimum and only after all other methods (rocking, cuddling, feeding, etc) have been exhausted. People who recommend letting them cry at only four months, particularly without any other comforts, show their ignorance. At four months, you still comfort to sleep. It is not a battle, it is not a boundary, it is not a manipulation. It's a basic human need. (In fact, babies at four months are not at all capable of cause and effect, which is required to manipulate someone.)
She is used to the motion of the swing - a crib is totally different. Elevate the head of your child's crib (we used empty baby wipes containers under the legs of our daughter's crib who had reflux) and try white noise and gentle vibration - a box fan on low pointed away from the crib, set up against the leg of the crib. Your child will still wake to eat at least once during the night typically at this age.
Since she has acid reflux, try putting a catalog/book under the upper end of her mattress and it will allow the stuff in her throat & nose to drain downward. Lying flat is dangerous as she could choke.
Meant to say where she wasn’t laying down flat in her baby swing.
The job of every baby/child is to push the boundaries until they get what they want. The job of every parent is to establish where the boundaries WILL be. When the baby/child gets used to the boundary and realises their temper tantrums and screams won't shift it, they accept it. Having once conceded ground, winning it back is a battle of wills but, as the parent, you have to win.
You're never too young to learn that making a fuss might net you your own way. Guess what? Your baby is smart and has figured it out. Show her who has the better developed intellect. Of course be kind about it, but just persist with putting her in her crib. Of course she'll cry, and if it goes on for too long a long time, pick her up and reassure her, then put her right back and go away. Let her cry again, pick her up really briefly, and put her back. Repeat and repeat. She'll get the message. It's not cruel but it's hard to do.