The dropdown menu list is awfully long. As a web designer, I seriously don't recommend this as it will badly affect the user experience. Is there an alternative?

You tell me :)

Maybe a box that shows the first 10 items and the user can scroll within the box and simply click on the proper medication or highlight it?

Bottom line is needs to be responsive design :)

What would you normally advise as a web designer? I want it to be end user friendly as well...

what about a search box, where the customer can type in thier rx name and search and it pops up automatically....kinda like what happens when you trype something in google search and it recommends searches?

As long as that isn't only what you were expecting to be designed. I'll work on something for you :)

Do you have any product or marketing images to attach?

No, not at all, I am open to the design. My only requirement is user experience...easy peasy :)

No I do not. Will have logo later but you can use generic logo for now

can you guaranteed your project?