H.W.
First off, A., this is really, really common. Your toddler is not doing anything out of the ordinary.
If you can, consider babywearing. I was a nanny to newborns, and then did child care while my own son was wee little. I nearly always had the babies in a pack, unless they were asleep. This satisfies baby's need for contact while keeping your hands free to help your 16 month old. Even using it for just a few hours a day can help. Make sure you get one which fits you correctly so you don't hurt your back. (I have more damage to my hips from carrying children on my hip for years than I do my back. So consider what will work without hurting your body.)
If you can, stop feeling guilty. Tell yourself that this is *good* for your son to not be first for your attention. This was one reason I did go back to work and have a preschool later on-- it was important for my son, an only child, to learn that he's not the most important person in my world. It IS a hard lesson, but will get easier as he gets older.
This is also a time to turn your attention to finding things which capture your toddler's attention. Below, I'll link to an article which can start you off. My observations were that sensory activities best fulfill a real need, and that you also need some forethought as to what is going to be doable for you and what's going to feel like too much mess to clean up.
http://handsonaswegrow.com/50-toddler-activities/
Be sure, too, to give your newborn time to sleep and be on their own as they develop. and never, ever leave them alone together. It is just too easy for a toddler to harm an infant, even if they don't mean to. Consider taking a shower when your partner is home in the mornings or the evenings. And also, when your partner is home, hand baby off to them and spend a little one on one with your son whenever possible. This will ease up over time. :)