Hi J.,
Welcome to the joys of motherhood. It sounds to me like your trying to figure out what is socially acceptable. Your son is 4 months old! When you are upset don't you want to be comforted? There is nothing wrong with picking your son up and loving him in his time of need. I have a 3 year old son and a 5 month old daughter and neither one of them have ever cried themselves to sleep. My children are just fine. It also may too much change for your son to deal with... formula and to swaddle or not to swaddle.
I understand your a first time mom and I am sorry if my comments seem harsh. It just breaks my heart to picture a baby left crying in a room all alone, when there is such a simple answer. I also am not too clear... are you putting your son on formula because you have an event to go to or because you don't produce enough milk?
My suggestions, take them or leave them, is to just love your son and do what you feel is right. Don't let society tell you what is right.