Clingy pets 😩

I recently rescued a stray kitten. The vet says she’s about five weeks old, so typically too young to be away from her mother. She’s entirely weaned, however, and won’t drink the kitten milk replacer I got from the vet. She eats canned kitten food and drinks water. She listens well and doesn’t cry during the day, and she’s gaining weight well. The only problem is that she can’t sleep unless she’s touching me. She’ll whine and cry if I don’t bring her in my bed, and when she’s in my bed, she just crawls over to me and snuggles up right against me. If I move her away, she wakes up and crawls back. Normally I wouldn’t mind, but it makes it super difficult to fall asleep trying to position myself around her.

Are there any ways I can get her to start sleeping away from me or is this something she’s just going to have to outgrow?

Pictures added just to show off my new kitten because she’s adorable!