This is exactly what happened to me in hospital. When my baby was born she fed well for the first 2 feeds then would not latch on at all. I had to express colostrum into a syringe and give it to her that was. Her blood sugars were checked with every feed and were low and didn't improve after a feed. After continuing to try breast feeding and baby becoming very upset I was persuaded to give her some formula in a cup. Baby continued to reject breastfeeding and was getting more and more distressed with every feed. I continued to express and gave her that in a cup. I was then told that I would not be able to be discharged if I was expressing and cup feeding. I found out later this was wrong. So after 3 days in hospital, being totally shattered from no sleep and feeling like I was starving my baby I gave in and gave her formula in a bottle. I continued to offer her the breast, which she wouldn't take and then formula feed her as well as giving her the little but I was expressing. I was in a right state as really wanted to breast feed and felt guilty that I couldn't do it.
Once I was home my midwife persuaded me to go to a breast feeding support group and it was a real turning point. I spent 2 hours in a private room with a consultant who eventually helped me to latch baby on. It was amazing as I thought it world never happen. Consultant explained that as I had a traumatic birth, baby was experiencing regular blood sugar tests and bring forced the breast by the consultant had all contributed to baby not wanting the breast. Plus I was also extremely anxious which baby was sensing. I was advised to not let baby get too hungry before each feed, do lots of skin to skin and also to bath with baby and offer the bracts and baby will relax and feel like it's back in the womb.
After returning home I continued to struggle to get baby to latch and contained to formula feed along with expressed milk. It was exhausting and I was very near to giving up and relying just on formula. Then I tried the bath and she latched on perfectly for the first time in 2 days since attending the support group.
After that things got easier. If baby was calm I could usually get her to feed. She preferred to feed lying down so would mostly latch on. If she was really hungry it wouldn't work to I would have to give her formula or expressed in a bottle. I also had to play catch up with my supply as is been using formula.
Now at 7 weeks old we have got there. My baby is mainly breast fed but I do still give her one formula bottle a day. This is because I exclusively breast fed her for a week and it was too rich for her. She was constantly popping and it made her sore. Giving her the odd bottle of formula meant that she stopped constantly pooping and restored balance in her system. I think she'd got used to the combination of formula and breast milk. So she's quite happy.
After nearly giving up breast feeding I'm really glad I didn't. But it was so tempting as it was so hard in those first few weeks. My advise is if you want to breast feed the try to persevere. Don't panic about giving a bottle and nipple confusion. Apparently if you express so that you don't loose your supply you have 4 weeks to get baby to latch. So try not to panic. Although it's not easy try to be as relaxed as possible when feeding. Give lots of skin to skin and try breast feeding in a warm bath. Try lots of positions. As I said my baby would only feed lying down in early days if breast feeding, she'll now feed in any position. Also if it doesn't work out then don't beat yourself up as at least you tried. Good luck and take care xx