I've never observed the "feeling sick" issue myself in periods of greater productivity, but that could be because I wasn't paying attention - I have "evening sickness" like you described roughly 2-4 times a month, and I end up just popping some paracetamol and feeling fine the next day. My blood work comes out OK on checkups, so I (and my doctors) guess it's likely some mild allergy rearing its ugly head every now and then.
I can share some things that I've found out over the years that are not helping:
- Alcohol. I tried that because during my one month-long super-productivity period I was also drinking socially quite a bit. After testing I ultimately rejected this hypothesis; regular alcohol consumption doesn't seem to help me get back to this "flow state" (and makes sleep worse).
- Sleep deprivation. Naturally, in the golden period I was doing so much that I slept irregularly and less than I should. So I tried sleeping less, but it didn't help.
- Music. I had a certain set of songs I was constantly listening to on my headphones as I made the world subject to my will. The songs still get me in a kind of productive mood, but the effect seems to hold for 5 minutes, not 5 weeks.
- Anxiety. Turns out having it is orthogonal to super-productivity! I had anxiety problems back in these golden times, I had them later on, over time I've learned to cope - but between low and high background anxiety levels, the super-flow didn't return.
That super-productivity I'm seeking comes with a very specific kind of feeling, like you're doing logistical parkour through your day. And now in comparison, lack of it feels like an engine that can't start. Or like those episodes in Star Trek where they can't stabilize some force field, and it keeps sorta-working, but blinking in and out. That's how I feel these days.