Mine are 2 years apart, and the second is 3 months now. I was surprised that the broken sleep is much easier to cope with this time. I think the whole life-changing shock of having a baby isn't there the second time, which is what i remembered and dreaded with the second but obviously a lot of changes, adjustments and sacrifices have already been made with the first one so you don't have to go through that again. I was very uncomfortable during the pregnancy so actually it was nice to be a bit more active with dd1 again after the baby was born, and I did feel more energetic than while pregnant.
I'm finding the emotional side of it harder than the physical. My dd1 was the centre of the universe for 2 years and naturally finds it hard to share attention. I feel guilty for turning her life upside down and guilty that the second will never get all the attention. Dd1 got her last 4 molars since the baby was born, which was REALLY bad timing! She's also in the process of a massive growth spurt and a sudden jump in her language, so she's all over the place. She's a great kid, but life is tough for her at the moment. It can be hard to stay calm and remember she's only 2 and dealing with so many changes. It's immensely frustrating when there's no pleasing her and I'm limited by the baby.
DH has taken dd1 to her grandparents for a few hours today to give me a break from it.
Bear in mind that everything passes eventually, choose your battles very carefully, don't worry too much about junk food and screen time for the older child, and remember to take pictures of the baby because the first weeks go by in a flash (albeit a difficult exhausting flash!). If you can, go to a toddler group. It's good to have contact with other parents, and for me it is extremely helpful to see families with a similar gap but a year or two ahead of me. I'm told by other parents, and can see for myself, that it gets easier after the first year, and being reminded of that once a week keeps me going!
It will be hard, but it is doable, and hopefully in a year or two will all get easier.