Tying a goat up 24/7 is animal cruelty. I understand it is a standard in your country - but you need to make a change. Your goats will thank you, they will love you so much for it!
I don't know exactly if they are dairy breed. People usually get them as they look so beautiful. They don't give too much milk that I am a sure. The milk maybe even not enough for their kids sometimes. So maybe they are not dairy breed. They are called Gulabi Goats in our country.
Thank you for the clarification. If her teats are soft, it may be hormones working because she is pregnant. Mastitis comes to mind, yet is is usually just one side.