Generally speaking, milk production is a supply-and-demand type of function, meaning the more you nurse or pump, the more milk your body will make, but in the short term right after delivering a baby, it's actually hormone driven. During pregnancy, hormone changes in your body were ramping up the milk-making factory and getting your body ready to make milk, and then after the placenta is delivered (whether it's by vaginal delivery or by C-section), that is basically turning the milk-making factory switch on and so milk starts to be produced.
You wanted to know what you can do to stop production after delivery, because you're planning on formula-feeding, and this is a good question. You do need to plan on it taking at least a few days for milk production to cease, because it's hormone driven. And generally speaking, after delivery, a mother will breastfeed and pump to stimulate production, but you want to do the opposite if you don't want to encourage that production. But you may have to pump just enough or manually express just enough milk to help your body feel comfortable as it get's the message that it doesn't need to make more milk. This will mean that every few hours, you may need to manually express or pump off just enough to the point of feeling comfortable, but not to the point where you empty the breast, because when the breasts are emptied, that's when it gets the signal to fill them back up again.
Ice packs can also help, so you can use cold packs, or gel packs, or even just a bag of frozen vegetables and place one on each breast after you've manually pumped or expressed a little bit of milk every few hours. And you'll only have to do that probably for the first couple of days. And then as time goes on, you'll slowly want to increase the amount of time you go in between letting off a little bit to the point of feeling comfortable, and just be really careful to not empty the breast when you do that. Again, just take off enough to the point of feeling comfortable. Instead of using ice packs or frozen vegetables, you can also use cabbage leaves, and you just wash them, and you strip the vein out, and you put them in the fridge and let them get cold, but cold or not, they can actually help to suppress milk production. So you just stick one in each side, just like you would a nursing pad, and let them sit for a couple of hours. At that point, they'll start to wilt and then you can replace them with new ones.
The reason why this process needs to be gradual and slow is that if you just did nothing about it and the milk is being produced, it puts you at risk for engorgement, and clogged ducts, and a breast infection called mastitis, and you want to avoid these things at all costs. So again, without sending the message to your body to make milk, just incrementally empty the breast to the point of feeling comfortable, and after a few days (maybe a week), your body will get the message that it doesn't need to make milk anymore. If a month goes by and you can still manually express a little bit of breast milk by squeezing the breast or massaging it gently, don't be alarmed. That's pretty normal.
If you do start to feel a little uncomfortable during the process of suppressing milk production, you can also take ibuprofen as long as your doctor says that that's okay for you to take. This can help with that discomfort and swelling that you might feel. Also avoid any breast stimulation while you're trying to suppress milk production, and this will involve wearing a good supporting bra - one that's not too loose, not too tight. Avoid binding the breast, because that's what your mom or your grandmother may suggest, but research tells us that that's not the best thing to do, so just a good tight-fitting bra, a sports bra would be a good example.
If a month goes by, or even a few months, and you find that you can manually express a little bit of breast milk, that's okay. That's pretty normal after having a baby. Don't be alarmed unless it has changed color or unless you notice any irregularities or differences in the breast tissue, areola, or nipple, in which case, you would want to bring it up with your doctor. If you have more questions in the future for me, feel free to ask them at Intermountain Moms on either our Facebook or Instagram pages, and recommend us to your friends and family too.