Okay, to anybody who might stumble upon this now, Android Studio is very, very, very weird.
Solution : Go to your build.gradle file and in your dependencies find the appcompat one, something like compile 'com.android.support:appcompat-v7:XX.X.X'
Change it to compile 'com.android.support:appcompat-v7:XX.X.+'
Then click on Sync Now on the top right of the editor. All the red squiggly lines should go if everything else in your code is correct.
Then go back to your build.gradle and change it back to whatever it was and click Sync Now
It should all be fine given that you have the latest version of everything or close to it.