Shulchan Arukh, Orach Chayim 332/שולחן ערוך·אורח חיים של״ב

11. That One Should Not Deliver an Animal on Shabbat. We do not deliver an animal [being born] on Shabbat.

22. We do not scrape a scab off an animal, nor do we lubricate it with oil. This is referring to when the sore is healed, in which case [scraping it off] will only be to pleasure the animal. However, when the sore is new and there is pain, it is permitted [to remove the scab].

33. If an animal ate too many horse-beans and it is in pain, it is permitted to have it run around the yard so it becomes exhausted and is healed.

44. If it has an attack of congestion, it is permitted to place it in water so that it will cool down. However, if there is a chance that if we do not let blood, the animal will die, it is permissible to tell a non-Jew to let blood.