is arthritis cause exhaustion?

Elen, anything that brings chronic pain can cause exhaustion. It takes a lot of energy to deal with serious pain on a daily basis, and pain often interferes with sleep.

Add to that the fact that you're caring for a new baby, which is a very tiring task both mentally and physically, and the demands on your body for nursing. I'm not at all surprised that you're exhausted all the time. Be sure you're eating well, getting plenty of fluids and resting as much as possible. Lie down when your baby is sleeping; this is not the time to worry about a messy house or cooking elaborate meals. If you have family or trusted friends around, see if they would take the baby for a few hours so you can get some uninterrupted rest. Pumping and using a bottle for a feeding now and then shouldn't interrupt your breast feeding with the baby.

If your tiredness continues, consider seeing a doctor to be evaluated for post-partum depression. It's much more common than we used to believe, and often the primary sympton at first is tiredness.

Good luck to you, and remember there are people who care about you here.

You also need to stay moving. The more you sit without moving the more the joint will stiffen and cause even more pain. Did you ask your doctor if physical therapy would be possible? Some places can do therapy in water which eliminates a lot of the pain.
Exercise also will make you feel better all around which should help you sleep better. Exercise also causes certain hormones and chemicals to be released which should help kick that tired feeling.