First, PLEASE do some research. Don't bring an animal home that you know nothing about, and just go about assuming they are like other animals.
Goats are ruminants, they have a 2 part compartmentalized stomach, and they rely heavily on friendly bacteria to help break down their food. Any change in food, it takes a full 23 days for their stomach to adjust to the change by adjusting the proper growth of the right kinds of digestive bacteria. Since you have brought her home already, and are just throwing whatever kind of food at her without knowing what to provide, chances of sending her into enterotoxemia are pretty high. Get to your local feed store and pick up some GOAT FORMULATED probiotics and get her on them right away.
The heavy coughing is most often a sign of lungworms, in goats. A good worming is needed, ivermec products do the trick, but will need done over a period of a couple weeks if she is coughing badly.
Thirdly, are you absolutely certain
she is pregnant, and has not already kidded? Pygmys are litte fat things, they have wide stomachs and they often LOOK pregnant even when they are not. Bottle raising baby goats is extremely common and selling a doe that has just come in to milk is not unusual. If that is the case you could be doing her a whole lot of damage by not milking her.
Please spend the afternoon reading up on information about goats, so you can properly provide for her. Feeding and Hydrating a Sick Goat Goat Health Information Pioneer Meadows Pygmy Goats: Pygmy Goat New Owners Manual Pioneer Meadows Pygmy Goats: Feeding Your Pygmy Goat How To Care for Pygmy Goats | Goat Health