When I open Camera, I can see the back camera is working but the front camera is not. When I press on the camera icon to switch cameras for a long duration, it shows 'AE lock'.
Can someone help me with regaining access to my front camera?
The camera's probably just stopped working and needs to be replaced. Check out ifixit.com for a step-by-step guide on how to replace it and then decide if you feel comfortable with the doing the repair. If not, there's probably someone in your area that can do it for you.
If it were me, I'd save any money I'd put towards a repair, back the phone up to iTunes, save the photos to my computer, and just upgrade to a newer iPhone.
AE Lock is simply a state you can put your iPhone camera in by holding your finger down on the main display for a few seconds to lock the aperture.
I think you may simply be missing the icon (aka Fat Fingers), or the upper right corner of your display is not working properly.
I would suggest trying/downloading a third-party camera app, many of which have the front/back icon in a different location, to test whether it's actually working or not.