My husband is lying...is he cheating?

So, my husband has been acting very strange. Anyways, we just had our first baby 2 months ago and sometimes he stays later at work. I nonchalantly will ask how was work busy...did you work overtime? Usually, he says yes or that he had to run some errands and comes home a good 3 hrs later than normal. So this is where I feel that he is up to no good. Also, he has been working a lot of weekends saying he is trying to make some extra money.

First off, we haven't had intimate relations in a long while because of the baby. However, there have been several opportunities where we had some time and he didn't even initiate or act Interested and then when we did he just wanted me to give him a BJ. Which struck me odd because that is not how our intimate relations have been and he has always been the one to initiate. Another thing is that he has stopped helping me wash my laundry...he use to wash mine with his and now he just let's mine pile up so I have to do it myself. Also, he is worried about how he looks and he going to the gym more which I am all for however, when I ask if I can join he is hesitant. Lastly, the kicker, I went into a coat pocket of his after I had been out of town for two weeks with the baby and found this condom pleasure sleeve which I have never seen before.

Also, the other night he was out later after work and when he came home he said that he went shopping to pick up some clothes for out beach trip. That is why is said he was later than usual. Problem is when he left for work I checked his bag of clothes he bought and the receipt was from last week...I saw the date. He wasnt out shopping that night he lied and I don't know why? I just would like some thoughts regarding this matter and how to confront him.