Hi Alohasoph.
I had a similar problem with my two, when they were the same age.
DS1 had been incredibly needy so I'd rocked him to sleep and held him pretty much constantly for the first six months of his life, but when DS2 arrived, I knew that I couldn't do that for him and look after DS1 too. So I got DS2 used to falling asleep by himself in his cot, and sleeping there by himself too. It's not too late for you to train your little one to sleep in his cot - you might even find that s/he sleeps better as a result.
I also had to sleep train DS1, who was used at the age of 2, to falling asleep with me in the room - which made daytime naps a nightmare, but it was only when DH was away for work for three nights, and bedtime went from 8pm to 10.30pm because DS1 wouldn't go to sleep without me, and DS2 was screaming for me, that I twigged that this situation was untenable. So I did controlled crying with DS1, which meant five hideous days and nights of howling, after which he would fall asleep by himself in his cot - I felt as if I'd been given two extra hours in the day as a result.
What I'm trying to say is that when you have two little ones who need you, you have to be more disciplined about the time you give to each of them. If the baby was your only child, then holding it all day would be no problem, but if it means that you are denying DS1 time with you, then I think that you need to find a way to put the baby down for naps so that at least then you can spend some quality time with DS1.
(BTW using a sling in incredibly hot temperatures must be so uncomfortable for you and the baby!)