iOS native photos app doesn't support dropbox sharing although you can open dropbox app in you device and add files manually. Make sure you have given dropbox permission to access photos.
Details:
Manual Upload
Step 1
Launch the Dropbox app on your iPad, and sign in to your Dropbox account if prompted.
Manual Upload
Step 2
Navigate to the folder on your Dropbox account to which you'd like to upload a file. If you'd like to create a new folder for your files, tap the plus sign at the top of the left column and then tap "Create Folder." Enter the name of the folder, and tap the "Create" button to create your new folder.
Step 3
Tap the plus sign at the top of the left column, and then tap the "Upload Here" button.
Step 4
Tap all of the files you'd like to upload to your Dropbox, as you can upload multiple files at once. A blue check appears in the upper right corner of the files you've selected.
Step 5
Tap the "Upload" button to upload the files to your Dropbox folder.
Automatic Upload with Camera Upload
Step 1
Launch Dropbox on your iPad, and log in to your Dropbox account if prompted.
Step 2
Tap the gear in the lower right corner of the left column to visit your Dropbox settings.
Step 3
Tap the "Camera Upload" tab, and then switch the button from "Off" to "On." Your photos and videos automatically upload to Dropbox from your iPad's storage.
source
Best Answer
Apple has a support page about this.
To import edited photos to your computer
If you want to view the edited version of a photo on a Mac or PC that doesn’t automatically import the edited version:
AirDropor email the photo to yourself.This will save a copy of the edited version on your computer, but you won't be able to revert to the original, unedited version.