Yes, it is very normal to feel the way that you do. You are in the grieving process and it all takes time. Some days, you'll feel okay, and others...well, it will take everything you have to muster up enough energy to get out of bed.
Take it one minute at a time, one hour and then one day. Do what you feel is necessary to keep yourself going. Don't sweat the small stuff....if something can wait a day or so, then let it slide if you are not up to doing it at that time.
Above all else, be kind to yourself.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.
