How're you doing now OP? I can say from my professional and personal experience that"it depends" (useful, I know!).
Well, if they are small and you can push them back in, they will probably go in 3-4 days. If they are rock hard and cannot be pushed back in, then anywhere from 2-12 weeks for them to go away by themselves. You can have a small procedure done to remove the hard lump inside them, and after this procedure you're looking at 3-5 days before they heal completely. The procedure involves a local anaesthetic which is a serious pinch, but provides good pain relief for about 1.5hrs. A small cut is made, which you won't feel, and the hard lump inside the hemorroid (the offending clot) is removed. It's a simple straightforward every day procedure and o ly takes a few minutes. You really should take oral painkillers at the same time as the local to provide pain relief for when the local wears off, which can be incredibly painful.
Applying ice, hot compresses and sugar altenately can help to reduce swelling of minor piles. While sugar is seriously messy, it does help quite a lot by osmotic effect.
Difene suppositories are your friend for a numb bum. Liquids and veggies only to eat, 2 Movicol a day and stay in or very close to bed and bathroom. Shower to clean and short soak in bath or sitz tub after every movement, and try to massage and push back in the lump every time. Avoid toilet paper, use wet wipes or cloth wipes. Don't use steroid containing creams for longer than seven days because from then on they worsen irritation. Glycerine suppositories can help if you feel the urge to go but are too scared to push (remind you of anything?!). When they get itchy DO NOT scratch. Rest a lot. Horizontal as much as possible. They can be seriously painful and do not underestimate how debilitating they are, it's not just you, ask for help and look after yourself.
Congratulations on the baby, and try not to do anything other than feed and focus on recovery.