Having a newborn baby to take care of can be marvelous,exhausting,lovely and crap all at the same time.
You are not being soft your being a human being who's just had her life turned upside down all whilst recovering from 9 months of growing a human being inside you,the strain of being in labour and giving birth,the pain that your milk coming in and breastfeeding can cause and to top it all off you have to be on call 24/7 to a little pink bundle that you have to cuddle,bath,feed,wind,dress,change nappies for.
It's still very early days please be kind to yourself,rest when ever you can,make sure your eating and drinking as well as you can,concentrate on doing nothing but feeding,washing and clothing yourself and your baby for the next few weeks.
If your DH is on board with getting up with the baby in the night then it's no one else's business,and like other posters have said going to work and getting proper tea breaks and lunch breaks,being able to go to the toilet when you want to and not having to think of anyone else,getting adult company and adult conversation all whilst being paid is a doddle compared to being at home with a newborn especially when it's your first!
I presume you should be having your 6 week check up with your midwife/HV soon?It would be a good idea to mention to them how your feeling just incase your anemic or low in vitamins either of those can make you feel really fed up and realy lethargic.
I hope everything starts to settle down for you all soon and that you all start to get more sleep,sleep deprevation is the worst(I have 5DC)and congratulations on your new baby 