ok some questions:

1. from where did you take the water in the first place?

in case you took it from a pond/river it might have been infected, if you are unsure use water purification tablets

2. i highly doubt you need the alcohol tincture for the threatment

did you try just steps 3+4 for alone?

3. you said PET bottles cause that sickness, so: did you try to drink the same ammount of water with canteens?

if you are so specific with that report one would expect you have ruled the rest out, if you have not, please test some more and update the topic or post a note

PS:
i also doubt you need to vomit, but i never got sick because of water, so idk, maybe its differnt from what i have experienced
so if you are testing, you might also want to just take some charcoal and wait

Vomiting doesn't help the sickness at all and actually harms you by draining your energy and hydration.

alright, you´re asking me why im so specific with this bug, well then, i spent a whole day to cure my sickness, to get information about problems in the past and what other people gave tips and tricks. so: i tried 3+4 myself, on others and they tried it on me. i could tell you the whole story and all this but that is just too uch what ive found, but heres the important thing and what i did:
-i drank out of 5 things, a CANTEEN, a PET, a POND, a WELL and a GASOLINE CANISTER.
-i ONLY got sick of the PET and the GASOLINE CANISTER
-i found out that the mechanics dont work: vitamin bottles, injection vial with syringe, purification tablets, water source (you can fill a gasoling up everywhere and fill atruck, but its still gasoline, but poured it into a pet and a cnateen and only the pet gave me the sickness)
-i used multiple ways:

1. charcoal tabs, then alcohol tincture and then vomiting
2. charcoaltabs, then alcohol tincture
3. alcohol tincture, then vomiting
4. charcoaltabs, then vomiting

only way 1. helped my, because as i said, YOU WOUNDS ARE INFECTED and THATS why you NEED alcohol because you need to CLEAN them, and DISINFECTION SPRAY didnt helped me and my mates. also you need to make it YOURSELF and becuse you dont have the option to go to someone and make "clean wounds" or something.

Vomiting DOES help, ofc you get a little bit of energy, hydration and health lost but your sickness gets out too. i vomit 2 times everytime i tried to cause that again and then i was good again.

as i said, i drank out of EVERYWHERE and only PET´s and GASOLINES gave me that, but the mechanics are broken, thats what i think at least.

and about the alcohol tincture:
if your wounds are dirty or already infected THEN you need a alcohol, because alcohol ures them and kills the bacteries, so its clean again. when it gets clean it can heal again even it doesnt make sence with water/gasoline but as i already said and im still gonna say it:
THE MECHANICS ARE BROKEN!

Its not just PET bottles. I first got sick from eating rice I looted from a friend who committed suicide because he couldn't cure this "whatever" it is. I the rice got me sick AND infected wounds (important to note that there is 2 things going on at once). I finally threw away the rice and stashed my stuff, and killed my self to clear it up. When I got back to my stuff, drinking from my canteen re-infected me. "Whatever" this is, can be spread.

Vomiting cures the SICK, but does not cure the infected wounds. Alcohol tincture will cure the infected wounds with 1 dose. Drinking/eating from a PET bottle, Canteen, cooking pot, bag of rice or box of cereal... basically any edible item that was previously used by you or someone else while sick will spread the sickness.

Once cured, emptying a tainted container onto the ground will bug your display to remove Energized and Hydrated and replace it with SICK. Logging out and back in will fix this, since you're not infected from actually drinking it.