TSA requirements are still that you may not have more than 3.4 oz of liquid in each container, and must all fit into a quart-size clear plastic bag. I recommend getting a reusable quart-size clear plastic bag to put all liquids under 3.4 oz of both yours and baby’s in. This should be in an easily accessible pocket or place that can be pulled out without unpacking anything else at airport security.
When traveling with baby, you might be traveling with liquids exceeding this amount that baby needs in the carry-on and on the airplane. TSA does allow certain items in excess of the 3.4 oz in reasonable quantities:
“Medications, baby formula and food, and breast milk are allowed in reasonable quantities exceeding three ounces and are not required to be in the zip-top bag. Declare these items for inspection at the checkpoint. Officers may need to open these items to conduct additional screening.”
I have, for example, needed to travel with pumped breast milk so that when I arrived at my destination for work I already had a stock of milk supply for baby. I brought four bottles, each with 5 oz of breast milk, in a black zipped cooler with a freezer pack. I just hand it to the officer, who takes it (and has never opened it), and sometimes runs a test on it, then hands it back to me on the other side of the metal detector. I’ve never been asked further questions about it, and have never had any issues or complications.
The same goes for formula, but I would recommend instead of traveling with a bunch of liquid bottles for the trip that you instead pre-measure the powder into separate bottles and mix it as needed with bottled water that you can purchase inside the airport after security, or that you can request from a flight attendant on board any plane.
The same also goes for any baby food (within reason) that you are traveling with, or any liquid medications that may be larger than 3.4 oz. Just make sure you tell the TSA officer about it as you place your belongings to go through screening, and do not send your milk through the screening belt!
Security regulations can vary in different countries and at different countries outside of the U.S. It is always best to check with the specific airline or airport you may be flying through that might be able to advise you on specific rules. However, I have found that in most places things like baby food/ milk are passed through without a problem.