It's said that a piece of special Puer tea was priceless, and many people are very into collecting Puer tea.

"It's said that a piece of special Puer tea was priceless" - very unclear what this means, to me. "There was once a special variety of Puer tea that was priceless"?

I feel it has a very different flavor compared with green tea, but apart from this, it's nothing special.

Probably not strictly necessary, but more natural - the way you have it, it feels like you've deliberately omitted the "it's", as if you want to speak very efficiently.

Black tea is also a fermented tea like Puer, and the most famous brand of black tea in China is Keemum Black tea.

Or "a famous brand". Unless there's only one famous brand!

I also bought some of that to drink.

More natural to refer back to "that" tea here, I guess because you've introduced multiple teas.

My feeling about these two kinds of fermented black tea is that the Puer tastes very mellow, rich and lasts a long time, while the Keemun black tea tastes a little lighter and doesn't last as long compared with Puer.

When you say the tea "lasts a long time", it sounds like you mean "it can be kept in a cupboard for longer before it goes bad", which seems like a slightly strange thing to mention here when you're mostly comparing tastes. Maybe you mean something like "the taste stays for longer on your tongue after you drink it"?

(Green tea is raw tea, which is not suitable for me because I often feel stomach-churningnauseous after I drink it).

Or "I often get stomach-aches after drinking it", "I often feel sick after drinking it", "it often upsets my stomach".

To be stomach-churning is to have a quality that makes *other people's* stomachs churn. "I watched a documentary about sausage-making today, and it was stomach-churning." And the churning of a stomach is more frequently associated with an emotional response rather than simple sickness. Not universally - you might say "My stomach is absolutely churning right now" if you were horribly sick - but it's more common as a reaction to something you saw or heard. "I have a story to tell you that will make your stomach churn."

Oh, and "not suitable for me" feels quite formal here. More natural to simply say "which I can't drink".