Lick Me, Like Me (2018)

Blurb:
Jooin is a young vet that charms pets and owners alike at his animal clinic. When a puppy and kitten are dumped at his door, he decides to raise them as his own. With love and care, the furballs quickly become full-grown -perhaps a bit too much, as they’re now two … hunky humans?! When your pets are this eager, it takes being a “pet lover” to a whole new level!

Source: www.anisearch.com/manga/46051