For the iPhone it may be necessary to launch iTunes, connect the iPhone, unlock it, then confirm to trust the computer on the iPhone, if prompted.
But the card should show in Photos, if it is visible in Image Capture.
Just to be sure, you already tried to quit Photos and to restart the Mac?
Which version of OS X are you running? There have been several reports, the the Import panel did not open on OS X 10.11.5.
If elements of the user interface do not show, that should be visible, I'd try to remove Photo's preferences files.
They are stored in ~/Library/Containers/com.apple.Photos/
Quit Photos, then drag the complete folder ~/Library/Containers/com.apple.Photos/ to the Desktop and restart the Mac, then try again.
Your user library may still be hidden.To reveal the hidden User Library:
- Quit Photos, if it is running.
- Bring the Finder forward by clicking on the Desktop or the Finder icon in the Dock.
- Select your user/home folder (with the house icon in the Finder sidebar)
- With that Finder window as the front window, press the key combination ⌘J to bring up the View options.
- In the View options panel enable ’Show Library Folder’. That will make your user library folder visible in your Home folder.
- Open your Home folder, then the Library folder, then Containers.
- Move the complete folder ~/Library/Containers/com.apple.Photos to your desktop. Move the entire folder, not just the contents.
Now restart the Mac and try again. If all is well, delete the folder from the Desktop.
You may also want to remove the file ~/Library/Preferences/com.apple.Photos.plist
If removing the preferences does not help, repair the library as described here: Repair your library - Photos Help