The tissue that makes up your labia is delicate and sensitive. Vaginal birth is very traumatic for your entire genital area, your labia included. Bruising, swelling and pain can be expected after delivery of your baby. Luckily, your body is able to heal and recover, given a bit of time. To add to your comfort once you leave the hospital, consider buying a postpartum inflatable cushion which looks like a ring doughnut. This will support your weight while limiting pressure on your genitals.
Your perineum is treated with ice packs for the first half day or so after delivery, then with warm sitz baths for the next few days. This treatment does a lot of good for your labia at the same time.
Labial swelling and pain will subside significantly after the first few days to a week; by the second postpartum week they should look and feel significantly better. If there is very little change by that time, you should consult your doctor or healthcare worker about it.