This app was mentioned in 9 comments, with an average of 3.89 upvotes
www.leagueofcomicgeeks.com and their app can do this, though it's not the fastest. Upload your collection, choose settings on each book, and check "Mark as Read". They show up on your personal "Read List" after that.
Doesn't have bar-code scanning, but "Comic Geeks" by League of Comic Geeks is a good app to keep track of weekly pulls. And you can move issues to a "My Collection", "My Wish List", or "My Read List" section.
League of Comics Geeks has an android app with a pull list, but it seems very limited.
My non-app solution is to use the Comixology Pull List, which sends a weekly email of releases I'm following.
What phone do you have? League of Comic Geeks is available for iOS and Android.
https://play.google.com/store/apps/details?id=com.LeagueofComicGeeks.app&hl=en_US&gl=US
I use "Comic Geeks" by League of Comic Geeks...it has a barcode scanner feature (that works about 80% of the time)
http://leagueofcomicgeeks.com/profile/mild111/collection
App on Google Play Store:
https://play.google.com/store/apps/details?id=com.LeagueofComicGeeks.app
Maybe League of Comic Geeks? It's free, and scans barcodes. It can sort into own, read, wishlist and pull list. It has a bit of trouble with older titles/barcodes, and you have to be very particular with wording in the search bar, though I find it to be pretty useful. Not sure if it has all of the sorting capabilities you describe, but it automatically sorts by publisher, title, volume number, etc. I hope this helps!
They have one, I think it's just called Comic Geeks
I use the Comic Geeks app.
https://play.google.com/store/apps/details?id=com.LeagueofComicGeeks.app&hl=en