With a little more digging I found that the problem was with the kbd process using tons of memory when I tried to write something. Google search with "kbd process" bring me a lot of useful links:
iOS & iCloud: Broken iCloud data causes kbd process to crash constantly and drains battery
What did worked for me was turning iCloud drive off and on again.
So it turned out I was dumb enough to turn iCloud Drive off and don't turn it on again!
Been using it this way for some 2 months.
But I've got the solution! (Mac only) I was digging through my iCloud files at
~/Library/Mobile Documents/ and found that there is a folder with the same name of the evil process.
I opened it up and decided to read some files, unzip here, convert plist there (see https://stackoverflow.com/questions/15179410/how-to-open-icloud-cdt-file) and voilá: in just one file, the process kbd tried to insert a word 147 thousand times. This entry was a correction from "mongolao" to "mongolão" (southern Brazilian idiom in Portuguese for a vulgar use of the word "retarded"), ironic. As there were lots of these files, I think with myself that the problem is that somehow the kbd process fell into a loophole, and I decided to delete all the content of the
Waited a few minutes for my mac to upload the changes, turned iCloud Drive off and on again on my iPhone and...... working! If I don't come back here to edit this answer it means this was it! (or I forgot something really stupid again)
Oh, and don't even try to boot up Finder to do this, be a good stackExchange user and only use Terminal. (Pro tip: Yosemite breaks the iCloud folder in Finder)
EDIT 3 (3 months later):
tldr: run the following on your Mac's terminal:
cd ~/Library/Mobile\ Documents/com~apple~TextInput
rm -rf *