Yep, normal I'm afraid. You're in the eye of the storm as far as baby number 2 goes. I've had 3 and the transition to 2 was the hardest thing of all. I feel for you, it is truly shit.
With hindsight, there were things I should have considered but I was too tired to make decisions.
To stop b/feeding earlier. I let them self wean at 12mths+ partly because they refused a bottle, and of course night weaning is really hard when you BF. I thing BF keeps you in a hormone fog, once I stopped I felt much better and energised.
Iron - I had low iron in pregnancy, and after a while started taking liquid iron as felt so tired (spatone?) which I think helped. So if you had low iron in pregnancy try this.
Drop your standards a bit - housework, personal grooming, time with friends, sex life, hobbies, career, family commitments - sad as it sounds, just focus on yourself for a bit. These will come back, just give yourself a few more months.
Do consider sleep training as PP have mentioned, I didn't do this and have had night wandering toddlers sharing my bed for best part of ten years now. It is not fun.
As I said, you're in the eye of the storm. Be kind to yourself, you're doing a great job.