I have not included any sketches because I want designers to come up with their own style. You should know that the entire user interface of the application is going to be driven by the style of this logo, so what you come up with is much more than just a logo.
My thoughts are that the logo is a bit more retro style rather than modern. I'm thinking classic medicine companies like 50's Alka Seltzer or Vicks. But I'm open to anything.
The logo doesn't necessarily need a icon or graphic behind it, but it may be best communicated with one. The 5-Minute portion should really stand out as this is a key selling point to the product. But of course, the value is headache relief, so the icon may include something in that arena.
Get creative and have fun; I'm eager to see what you come up with. My preference is to have this logo illustrated / vector rather than graphical, but you can submit whatever you want.
As entries come I will provide prompt feedback and guidance around what I like and dislike.
Finally, whoever is chosen to do the logo may also be tapped later to work on the user interface screens for the app. I've already done the wire frames and have begun development on the app, but have not built out the graphics for the UI.