What colour space is the image in? If it's in RGB and you send it to PDF with no colour conversion then it's going to look different on screen than it does on print, because it has to be converted to CMYK which is a different Gamut to RGB.
You should talk to your printer about what colour destination to send to. US Web Coated couldn't be what you need unless you're sending to a Web printer, like for newspapers.
Most likely you'll need US Sheetfed, Euroscale Coated (or uncoated)<depending onn stock of paper>, or Coated or Uncoated Fogra (again coated and uncoated refer to stock of paper)
When you make the PDF in the output section of the dialog box you should be possibly sending your PDF to one of these Destinations.
I guess the only time you wouldn't would be if in Photoshop or other program that you converted the image to CMYK and used one of the destinations as the profile and then imported that to InDesign, then No Colour Conversion would be ok.
But I don't think you did that.
Sorry for the short reply but I haven't got much time to explain further. If this is over your head or I've only half explained everything I hope some others can help you out.