I'm going to use and instead of but when it comes to building a sentence with two conflicting ideas because that is actually closer to the way I usually feel.

Example:
It was an excellent day outside but I was still feeling like shit.
is now
It was an excellent day outside and I was still feeling like shit.

Using but in such sentences is something I've learned to do from reading other people's work. It seems like copied behaviour, for me at least.