Your difficulty urintating after birth probably had to do with tired pelvic floor muscles, dehydration, and/or pelvic floor trauma.
So, do those kegels, squats, and go for walks, or even better yet, walking up and down stairs, to strengthen your plevic floor muscles. Good pushing technique--mother directed as opposed to the pushing where you push as hard as you can, holding your breath, for the count of ten. Stay off of the birthing chair, especially if you are a shorty. This can cut off the circulation to your perineal area, and increases swelling. Spend as much time in warm water during labor and birth as you can. Drink plenty of fluids during labor and post partum.
After birth, if you can't pee, get into a tub full of warm water and try to pee there. You can also try to sit on the toilet and put a couple of drops of peppermint oil in the toilet; sometimes this stimulated mom to go.
I don't know the situation with your first birth, but don't let people pull unnecessarily on the placenta. There is a difference in applying traction to the placenta to see if there is any give to determine if the placenta has already detached and is sitting there, and tugging to ttry to get it to prematurely detach from the uterus. Nurse the babe, or at least put the babe up to the breast. The babes lips only have to brush the nipple to release oxytocin. But, if you are stressed, oxytocin release can be inhibited, so surround yourself with supportive people in a calm environment.
Hope some of this has been helpful! The other replies are also very good; I just wanted to add some ideas that popped into my head, as well.
Lori
eta: get ice on that perineum right away, even before th placenta comes, if it is possible, to prevent difficulty due to swelling. We make our pads by putting a maxi pad under a running faucet (do saturate it, it will be a brick) and putting them in the freezer. Some of our clients have put comfrey tea on the them, or watered down witch hazel instead of just plain water before freezing. These feel great and help control swelling, which in turn helps control pain and eases difficulty in urination that is due to trauma to the tissues.