Here's what you won't find in American pharmacies.
We went to a farmacia somewhere in Liguria last month because the medical tape I had used to tape up my foot for plantar fasciitis caused both a long ugly blister and a severe allergic reaction to the tape's adhesive. It was kind of an ugly mess, and we wanted some cortisone ointment and cotton gauze and some extra large bandaids.
The woman at the farmacia really, really wanted to SEE it so she could help us better to get what we needed. I might have shown her, too, except that I had just spent a lot of time carefully wrapping up my foot with all the bandaids, etc. that we already had, plus I was a bit embarrassed to take off my shoe and sock. But can you imagine someone at CVS wanting to actually look at or even talk about whatever your gross problem is? It must be great to have a sort of mini-ER in every farmacia. On another trip, the pharmacist and my husband had a lengthy talk about exactly what my cough sounded like.
Anyway, the only products we haven't been able to find in Italy are scent-free soap, shampoo, sunscreen, and laundry detergent. Almost all apartments we have rented (mostly Airbnb) have provided all of these things (but perfumed) so you may not need to buy these things right away.
Haven't seen anything like Mucinex (but didn't ask for it either) and still find it kind of hard to figure out the kind of sanitary products I want just from looking at all the packages and asking my husband to translate all the words (really a fun activity!). Ibuprofen seemed kind of expensive but each pill was twice the usual American strength.
The downside of buying products while traveling is that you will probably have to buy larger sizes than you really need and then carrying them around for the whole trip. We usually take very small amounts of the "might need it in the middle of the night " OTC medications in tiny plastic labeled ziplock bags.