Sorry you're feeling crap, but the truth is you could have many more weeks of this to go - do what you can to survive. If you think TV and lights work then do it - you can worry about a routine later.
DS2 is 5 months old, we kept him downstairs with us until our bedtime (letting him sleep on a pillow after feeding him on sofa or in moses basket) until 10 weeks when we took him upstairs at 7pm, that wasn;'t working and after 4 weeks, we just took him back downstairs with us until bedtime.
last week, we started again with upstairs and he's taken to it okay now and is having a nap at 7:30pm.
Don't worry about the bottle of formula and guilt - it won't hurt, and some bfeeding mums I know always give a bottle of formula about 7pm (so their OH can get involved in bedtime routine). On the other hand there is no evidence at all that a bottle of formula will help him sleep better. At 3 weeks their tummies are tiny and milk gets utilised very quickly and they need fed more. Additionally their digestive system takes a while to mature and they can have lots of tummy pain the first 3 months which stops them sleeping well.
On the plus side - it does and will get better! Enjoy these moments, wear a sling round the house and see if that helps him nap better (better naps often mean better night time sleeps), use tv/white noise if it works, feed him to sleep, rock him to sleep, use the pram to help him nap, co-sleep - basically try all the things that work that people tell you not to do - do what you can to get through, babies can get into a routine at any age, don't worry about it now.