A couple things that may help--
First, try to pee often during labor--every hour if possible. If your labor is several hours long, and you find that after 2hrs you can't pee normally (can't pee at all, or only pee a tiny bit) then you can try some aids to peeing: a couple drops of peppermint essential oil in the toilet bowl; running water while you pee; trying to pee in a hands and knees position (in the tub or over a chux pad); sitting to pee but holding your belly up somewhat; peeing in warm water (tub or shower).
2nd, try to pee within an hour or 2 of giving birth. Same techniques as above can be used to help the flow if you need help--but especially after birth it can help to hold the belly up/in some: place your hands across your belly, very low (between pubis and navel). Now use some pressure to bring the belly a little upward, and an little inward toward your spine. This can reduce the weight/pressure on your bladder/urethra that can block urine flow.
Remember, either during labor or after birth, that rather than straining or pushing to get pee to come out, it's better to relax and think about letting the pee out, just allowing it to flow, deep breath, put your attention on relaxing the whole yoni area, let the flow start.
Keeping the pee flowing regularly can prevent a distended bladder. A distended bladder tends to hang up placenta delivery, and uterine shrinking after birth, and leads to greater problems with peeing--and swelling-- down there.
Also, and maybe even more important--you may want to push more gently during 2nd stage. Of course, follow your own body's cues...but I tell women, 'breathe when you can, push when you have to'--this can really help in letting birth be more gentle and less forceful, which means you will likely swell a lot less in the first place. I find that some women, once they have that urge to push, will push with all their might and main, hold their breath some, try to get as many pushes as possible into one contraction. But this is not necessary--you do NOT have to *resist* the urge to push, I'm saying to really *follow* it, really listen to your body and just allow those contrax to occur naturally. Breathe into the contraction, let the sensations move you (instead of 'trying to work it'). You will most likely do some bearing down! Just not as much. Remember that the relaxing fully in between contrax is just as important to birthing the baby as the pushing is...really truly! Follow the cues you get, trust yourself.
You might also try pushing on hands and knees (or kneeling, leaning against couch/bed), or sidelying....to reduce the pressure of gravity and bring baby a bit slower. Main thing here is, get into the position that *feels right* to you. It really could be anything at all, even standing up, anything at all if you are following what feels right to you.
I don't know what your other birth was like, so some of this info might not seem to apply at all. But since you said you were in a hospital, I imagine that you were in that hospital birth position of semi-reclined, and that you were pushing under direction from others instead of following your own instincts. You were probably pushing to a count of 10 or more, as hard as possible. You may well have started pushing only because they told you that you were fully dilated--but it's really best in most cases to push only when you feel the urge to push! Those hospital policies of pushing do tend to make many women swell quite a lot! I've never seen that kind of swelling when a woman follows her body's cues with pushing.
