Why not use the actual Instagram API? https://instagram.com/developer/endpoints/likes/
Why spend time parsing the HTML when you get that information straight from the source.
You can authorise using OAuth (https://github.com/dongri/OAuthSwift)
You could retrieve a list of users who have liked an image using the call below, you can then derive the 'like' count from this:
https://api.instagram.com/v1/media/{media-id}/likes?access_token=ACCESS-TOKEN
Alternatively if you want more information on the media, you can use the following endpoint:
https://api.instagram.com/v1/media/{media-id}?access_token=ACCESS-TOKEN
Details here: https://instagram.com/developer/endpoints/media/#get_media
Here is an example of a swift app using the Instagram API, you can check out the project on GitHub to see how it works.
https://maniacdev.com/2015/01/example-a-swift-based-ios-instagram-photo-downloader-and-browser
EDIT:
You don't need to authenticate as a particular user to use the methods you need.
Login to instagram as yourself:
https://instagram.com/accounts/login/
Register a new client: https://instagram.com/developer/clients/manage/
Use your new client id with requests instead of your access token:
https://api.instagram.com/v1/media/{media-id}/likes?client_id={CLIENT_ID}
or
https://api.instagram.com/v1/media/shortcode/5FcnSATPa4?client_id={CLIENT_ID}
You can make up to 5000 requests per hour with your client id.
You can play around with the Instagram API here: https://apigee.com/console/instagram
Just remember to use your client id.