There is no need to use clipping paths for indesign, just put your
object on a new layer, delete the background layer, crop the
transparency (Image>Trim set to transparent pixels) and save as a psd file.
In indesign use File>Place to put the image in your document.
Your path is sort of "inverted". In Photoshop, select your path with the white arrow, then select the pen tool again. Look on the path pallet and you will see a white and grey preview of the path. I bet that it's white with a grey square where your lipstick shape is. It needs to be inverted from that. So now look in the options bar. There are 4 "path mode" buttons at the right hand end of all the options. The usual mode to use is "compound". You may have it set to "minus front" or some other mode. Click the buttons and watch if you path pallet icon changes. For the future I recommend the button on the far right "compound" be your default.
Hi there...thanks so much. Your tip about the wrong path being selected was spot on! it works fine now. Thanks again!