N.J.
I have a 2.5 year old and a 12 month old. They are 17.5 months apart. Right after I had Isaiah, I went through kind of the same thing. My oldest son was always wanting me to hold him, and generally being very 'needy'. I found myself getting a little overwhelmed because of my youngest and my oldest both wanting all my attention, all the time.
What worked for me, is for like a week, when my older son wanted me to hold him, wanted me to play with him, whenever I possibly could I just did it. It really helped, and after that week he realized that he COULD have my attention when he wanted it, and he stopped being so clingy. It was hard, I will admit, but it really helped.