If you want to cut a blood vessel, you should go for your femoral artery, or your brachial artery.
Ibuprofen is OTC for a reason--it will not kill you. Liver damage isn't a game you want to play; I can tell you that as an alcoholic approaching 40. Organ damage is DEBILITATING. [EDIT: I got the wrong organ. Any human being is responsible to source their own data beyond social media commentary... in case that needed to be said (I am responsible to try to be accurate but y'know as your average idiot I'm not that responsible)]
It will not make it easier to kill yourself if all of the sudden you chuck on a whole bunch of trauma, pain, nausea, etcetera. Not at all.
I understand risk taking behaviour and all that. Hell I've got adverse scar tissue in both of my wrists, so that means sometimes I have limited range of motion and all the time I am in pain in my hands and forearms. It's from cutting my veins. The more superficial wounds didn't fuck with any of the functional shit.
I dunno, you do you but you're not planning a lethal activity. You're planning a high risk activity, and the consequences will be shitty and they won't go away and they won't make it easier to kill yourself if your stated goal is to do that.
So... consider that as you will.
EDIT: hanging I did not bring up because it's simple enough to accomplish and has less chance of lifelong debility but still fails all the time so y'know at least do some planning. Probably don't even try the other two.