The legal bit: https://www.exteriores.gob.es/Consulados/santiagodechile/es/Comunicacion/Noticias/Paginas/Articulos/20220512_NOT.aspx
Yet... if you bring non-classified medicines (most of them, except narcotic and/or psychotropic medication) and in an amount suitable for personal consumption for the length of your trip, you shouldn't have any problem. In fact, it's unlikely you're going to even be asked about it. Still, it's best if you carry your prescriptions with you, just in case -officially sanctioned by a registered doctor, of course!
Furthermore, some of the medicines you bring are likely sold here as well -with the same or another brand name-, and some are even sold over the counter without a prescription being required (ie. Voltaren). And on an extra note: far cheaper than you'd pay for it in the US, that's for certain!
If you're carrying a classified medicine, out of precaution and to avoid delays at the airport, you might need to follow the directions indicated in the link above.
A final word: generally speaking, our rules here in Barcelona -which are in fact EU rules- are far leaner than those in the US when it comes to medicines and drugs.
PS: The link above is for the Spanish consulate in Chile, but don't worry, it applies to travellers from the US as well.