pics are helpful. the teats don't look unusual, that's what they normally look like when they're not too full.
if they get chapped, dry, crack, or you see any bleeding, you can dress them with bag balm - it's kind of oily jelly and it will soften the skin and help prevent and heal cracking... sort of chap stick for teats. these don't look like they need it, and sometimes the kids don't like the taste of the bag balm so it may interfere with nursing, so I don't use it unless it's needed.
as to milk... I don't see a lot of it here. some goats produce barely over what the kid needs, so if the kid is drinking often you won't see much accumulation in the bag. however, sometimes they're not producing enough and the kid can starve, so you need to make sure she's producing.
here's how to milk so you can check to see if she's producing:
pinch the teat completely off at the top, near the udder, using your thumb and index finger near the palm. this keeps the milk from retreating back up into the udder.
starting with your index finger, curl it tight around the teat pressing it against your palm, pressing the milk in the teat downward. middle finger next, then ring finger and little finger... so you're "rolling" the milk down from the top of the teat to the tip and out. if you get a good closure at the udder, and roll downwards, you should get milk out.
it's kind of like getting the last of the toothpaste out of a tube, start at the top and press the milk down, don't give it a way to go back up.
if you aren't getting any milk out of the teat after doing that, she may be dry. milk produced will flow down into the teat before it builds up in the udder and the udder starts to inflate. there is some natural mass in the udder, more on some goats than others, that may make it look somewhat full even if she's not producing. if the teats are empty and the udder looks full, it's not milk. mastitis scaring can also create bulk, but won't produce milk. both of these things can be true on one side and not the other, so you might have only one side working, or you might have mass on one or both sides but no milk.
you need to check the kid's belly to see if it's getting milk... belly should be gently round and feel full and a little springy or firm when you press on it. if it feels empty, or loose, or tucked up, you need to get some kid milk replacer and bottle feed or you will lose the kid.
what are you feeding mom? how's her weight? can you feel backbone / ribs / hip bones when you run your hands over the top? if she's thin, she'll need extra feed, some grain, to support herself and make milk. if she's feeling poorly and not eating or drinking she can stop producing, and she may or maynot restart making milk once you get her squared away.
biggest concern right now is 1) is the doe producing and 2) is the kid getting enough milk.
the kid will try to nurse even if there's no milk, so his trying isn't proof that he's getting any. you can lose them in a day if there's no milk, sooner if it's cold, so this is something you need to check right away.