Thank you for your question. My name is***** I have been a small animal veterinarian for 14 years and I'd like to help with your question.
Can you tell me a bit more.... Did she eat well and feel good initially after the kitten was born? Have you tried to take her temperature to see if she has a fever? Have you palpated her mammary glands?
At 4 weeks of age the kitten should have it's teeth and be starting to eat solid food. He probably won't need any bottle feeding. Try some canned kitten food diluted with warm water. The most common thing to cause a momma cat to feel bad at this stage is mastitis. As the kitten is getting it's teeth and nursing and mom starts trying to wean the baby, the masitis can form. Usually you can tell that one or more of the mammary gland is firm, red, or painful. There are other potential problems that can develop at this stage, but mastitis is the most common. They can get metritis at this stage which is an infection in the uterus, especially if they didn't pass the entire placenta when the kitten was born. It is also possible that something entirely unrelated to the pregnancy could be going on.
I would wean the kitten, try to get it eating solid food. I would palpate the mammary glands. If they are swollen or painful then this is likely mastitis. It is usually pretty easy to treat, but you would need to see a veterinarian for a prescription of antibiotics. If it is not mastitis then you will likely still need to see a veterinarian to evaluate her. I hope that help, but if you have more questions please let me know.
Were both mom and kitten healthy previously? Did all this just begin? Any vomiting or diarrhea?
A 4 week old kitten should be at a stage where he is becoming active, exploring, starting to play. They won't often go right for the food if it is new, but they will usually smell it because they are curious and once they feel hungry they will start to taste it. I'm not sure what to think because you describe him as rest less and then as not wanting to move. Either way, that is not a sign of a healthy kitten
It sounds like both of them are sick, not just mom. Was mom vaccinated? If it is both of them then something toxic or infectious is more likely. I suspect you are going to have to take them to a veterinarian for some tests to know what to do next. Can you get them seen by a veterinarian today?
I'm glad you were able to make and appointment. Until then, try to keep the kitten warm and hydrated. Use the milk if that is all the kitten will take. You might even add a little extra water to the milk just to make sure it is getting enough water and not getting dehydrated.