Hello, I am Dr Helen, a UK doctor.
I'm sorry to hear you are feeling so unwell.
Certainly as a new mum who never gets a full night's sleep this is not going to help. I suspect you are feeling quite exhausted a lot of the time.
Much of what you describe could be a viral illness you are struggling to throw off. The flu virus for example can leave you feeling very low for some weeks.
As you are breastfeeding you can get mastitis, infection within the breast that can make you feel unwell with flu like symptoms. Usually it is obvious if you have this as you have a painful, red area over the breast that is tender to touch. If you do have anything like this it needs antibiotics to settle it.
As these symptoms have gone on for 4 weeks it would be prudent to have a check up by your GP. You may be anaemic, or your thyroid gland may be underactive, as both these conditions can cause some of the symptoms you describe. A simple blood test can look for anaemia and check your thyroid function.
I hope this helps and that things improve very soon.
I joined JustAnswer in June 2013 and am a UK doctor. I have been qualified for 23 years and have widespread experience in GP and cancer care.