plenty of Swiss have similar problems, and there are so many tourists from all over the world who have these issues too.
There are two very large supermarket chains in Switzerland (and a good handful of smaller ones) with similar departments you will find in a US supermarket, so lip care and hand care, especially in cold season and ski season, eye drops, nose sprays etc. Products are as good as or better than near your home. The two are Coop (pronounced like kope) and Migros (pronounced like mee grow) and have excellent own brand products.
If they don't have what you want, a pharmacy will.
There is a small Coop in Mürren, a larger one across the road from the train station in Lauterbrunnen, a huge one with a restaurant across the bus station from the train station at Interlaken Ost where you change for the train to Lauternbrunnen.
There is a whole Migros complex with a huge Migros, and ancillary stores across the road from Interlaken West station.
You'll be fine.