Q: No import option for SD card or iPhone

Do the card and the iPhone appear in the sidebar of Photos, when you reveal the sidebar with ⌥⌘S?

Sorry, the "S" was missing after ⌥⌘S for "Show sidebar".

Photos will only show a card or the iPhone, if the device contains new photos that have not yet been imported. The import could have happened by iCloud.  Image Capture will always show the devices, because it does not check for already imported photos.

Have you tired to take a new photo and to use a different card, to see if the card then will be recognized?

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

You write, that Image Capture sees your iPhone and the card.

Try to set in Image Capture the Photos.app to open, when you plug in your iPhone or your card.

• Connect the iPhone and insert a card.
• Launch Image Capture.
• Select your iPhone in the devices list and click the actions menu at the bottom of the sidebar.

In the "Connecting this ... opens" menu select "Photos".

Do the same for your card.

Eject both devices, quit Image Capture, then connect both devices again.

What happens?

Can you import any photos at all into Photos, for example from your Desktop?  Drop a few photos on the Desktop, launch Photos,  and use the command "File > Import". Select the Desktop in the file chooser panel.

Do you see Import buttons for files from the Desktop?

If not, test with a new Photos Library, created for testing.

• Launch Photos while holding down the Options key.
• Select to create a new library from the Library Chooser panel.
• Try to import photos.

What happens?

If even a new library is not working, reinstall the system.  That is the only way to reinstall Photos.
reinstall by booting into Recovery as described here:   OS X: About OS X Recovery - Apple Support

You may have installed some incompatible software, that is blocking the import window in Photos.

is the problem system wide?  Have you tested to import from a different user account?  For example the Guest account?   https://support.apple.com/en-us/HT204443

So it is system wide.

Reinstall Photos by reinstalling OS X.

I'd try first, if the Combo updater will suffice to reinstall Photos, download and install on top of your current system, see this link:  Download OS X El Capitan 10.11.5 Combo UpdateThe OS X El Capitan 10.11.5 update improves the stability, compatibility, and security of your Mac, and is recommended for all users. May 16, 2016

If that does not help, boot into Recovery to reinstall also the basic system parts:  OS X: About OS X Recovery