I had DD when DS was 2.7 yrs. I felt just like you and it's awful isn't it.
I breastfed too so it was wall to wall C.beebies and up until 2.5, he never watched any TV as I was always out and about with him. I had him at activities and groups everyday and was very active.
Suddenly I had a very demanding, screaming baby with reflux, an under active thyroid which was wiping me out completely and I didn't know I had it and I basically hardly went out for her first year
.
Even when he started nursery when DD was 8 months I used to not take him because I was so ill.
I finally got the right medication and got back to normal this last few months and we are out all of the time and he is in nursery every morning.
I know it was me who worried too much though. He is perfectly happy and loves his little sister (most days). There has been no damage done.
In your case it will be a matter of months and things will pick up again and he will not remember a thing. Just get the TV on, keep chatting, stop giving yourself grief. It takes a bit of adjusting when you sudddenly find you have to meet the needs to two and the guilt kicks in.
This will all get easier I promise.