Crazy.
That's extremely uninformed, in my opinion. "Let's just administer a pain killer for EVERYthing that is wrong." Jeeeez Louise!
There is a reason that there are a lot of different Tylenol formulations available (or at least there used to be---last time I went looking they had pulled a bunch of Tylenol products from the shelves due to re-labeling issues by the manufacturer or something, according to my pharmacist). Tylenol. Tylenol cold. Tylenol sinus. Tylenol PM. You get the idea. They are all pain relievers with something extra to treat additional symptoms that aren't pain.
If you don't have pain, why bother with the Tylenol? Just go for whatever treats that specific symptom! Take an antihistamine if you are congested, but no need for pain meds if you don't hurt or have a fever.
No, you are NOT crazy to think this is overboard. If she just wanted to give her SOMETHING to treat symptoms, then she is just one of those people who medicates every condition (My husband is like that, I am not. But at least I can understand that.) But treating every condition by giving Tylenol for every condition is just nonsense.
ETA:
For the record. I am not "anti-medication", but I am one who waits a long time before giving anything. Most of the time it ends up unnecessary. My husband pops an Advil at the first sign of a headache. Or Pepto at the first rumble of the stomach. He gets aggravated with me when he asks how my day was and I say something like, "I've had a headache off and on all day".... (He takes it as a complaint and then says "well did you TAKE anything for it?"). Uh... nooo... usually they fade away and I don't even realize when and come back the same way..slowly and almost unnoticed until, well I notice. They aren't that bad. I RARELY take anything, and they go away without disrupting my day at all.
But, I also am one that has the full arsenal in my medicine box in the top of the pantry. EVERY variety of tylenol/advil, EVERY version of cold/cough medicine (with and without acetaminophen/ibuprofen, with and without expectorants), expectorants only, cough meds only, sore throat lozenges, plain tylenol, plain advil, actual aspirin, zyrtec and allegra...because I want to treat the symptoms that are present, not random stuff that isn't.
I would lose it with someone dosing my kids with tylenol for any/every issue.