Swollen finger

Have you went to the hospital

I wouldn't have thought a hospital visit would be needed for this as it doesn't look like an emergency (as in life or death). A visit to the doctor is probably the best way to go for this as it might be infected a bit...I'd only head to the hospital if you can't get a doctor appt or if baby also has a raised temperature

They look like hang nails or ingrown nails
Soak their hand in warm water with epsom salt, after bath when skin is soft try to clip the sides of the nail/ skin. When cutting nails try to cut across. You can apply some vitamin e oil to the area too. Cover the fingers with bandages to help it heal and not get infected. If it’s hot to the touch I would call their doctor to make sure it’s not infected.

It looks like it's coming from the fingernail. I'd make an appt with the Dr so it doesn't get infected.

I’m a nail tech lovely so seen this before it’s just a hang nail (skin at side of nail) that’s pulled and got infection. Just keep it clean with salt water and pop some savlon/tea tree any antiseptic you can to keep it clean. It will heal itself xx

Ingrown nail and/or paronychia Aka infection of the nail, both can be painful I would take her to the dr asap to resolve it. I had a nail infection on my toe from an ingrown toenail and it was causing a lot of pain even radiating up my calf