Very normal OP. I have three kids now 10, 7 and 2.
When dc2 was born I felt such sadness for my firstborn. Then when dc3 came along, even though there was a bigger gap, I felt it for my second born.
It's an aching bereft feeling and I used to cry when I looked at the child who used to be 'the baby'.
But it does pass and then you can't imagine it any other way. And the baby becomes a cheeky, physical toddler too!
When you've just had a baby your emotions and hormones are everywhere. Also humans don't like change and even if a baby is very wanted it takes time to adapt to new relationships and routines. But it is so very worth it. I love seeing mine together, playing and protecting. Yes there is jealousy and bickering too but that is also normal!
It's okay to indulge the baby. I know a lot of people ignore the baby a bit to focus on older one but it's important they see you love and care for their baby sibling because they will mimic this. They trust you and trust that this is right. Get them involved.
In the very early stages it's okay if another caretaker,Dad or grandparents, help with the older one while you get to grips with feeding and rest. As long as you carve out a bit of time for your older one where you focus on them. Maybe Dad could walk the baby and you cuddle up and read a story or watch a favourite programme. It really doesn't have to be big gestures just now.
Also don't worry if the older one rejects you for Dad a bit. Now mine are all past the baby stage it's much easier to give equal time and attention and I used to show my older two pictures of me breastfeeding them and carrying them in a sling. They come to understand that babies need a lot of practical care but your love is boundless and there is plenty for all!