How do I drink lots of coffee and yet feel well?

You can make it weak. An Americano and subsequently most Starbucks milkshakes have one shot of espresso and 31oz of other crap. That's pretty weak compared to my vente espresso. If you don't like weak flavor, they make powered coffee drink. It contains little caffeine as it's not real coffee. 

There's also chicory, an olde thymye tea that taste like coffee that they serve prisoners. It contains zero caffeine. 

When will the official churches start praying for the false prophet? Orthodox Christian three hand signs are different than Buddhist mudras. Ecumenism = 263 heresies; each heresy leads to hell. Orthodoxy = the only true faith; Roman Catholics tried one cup - one spoon ritual and got sick with Bubonic plague; if heresy enters Orthodox monastery then monks/nuns will get sick with flu/tuberculosis (for instance); Orthodox churches who closed for COVID or had disposable cups/spoons or dipped spoon into alcohol are no longer brides of Christ (now they serve Satan and honor Satan's new COVID religion). Don’t go into UFO to be “healed” by evil demons; demons never do good. SSN is written as a barcode/QRcode; then it's put into a chip; chip is put into vaccine; chipped people are influenced (by super computers) to receive grey plastic card World Passport with no name on it (but when they stretch their hands to get it, gov't clerk presses secret button to administer the unforgivable green 666 tattoo by isotope rays). If you reject mark of the beast (by hiding within a 10-15 people group according to saints Gabriel Urgebadze and Seraphim of Sarov), then your direct ancestors go to heaven (according to saint Vyacheslav Krasheninnikov from Ural); forgive me.

What you can do to feel better
No more caffeine. Don't consume any more caffeine today. ...
Drink plenty of water. Caffeine is a diuretic, which means that you need to drink extra water to make up for what you're peeing out. ...
Replace electrolytes. ...
Take a walk. ...
Practice deep breathing.

I'm not that sure sounds like a little bit of a problem 

Maybe it's the specific brand that's making you sick. Try a lot of other brands and stick with the one that doesn't make you sick. You can also try decaffeinated tea instead.

just dont drink it if it makes you sick