Where can I edit my public profile?

To edit information in your profile, simply click on your display name in the top-right menu bar. A dropdown menu will open, from which select 'My Accounts'. Your account settings page will open where you can manage your personal information, expertise, skills etc. You can even change your profile pic from this page. 

But to change your timeline simply go to your profile page by simply clicking on your display name in the top-right menu bar. A dropdown menu will open, from which select 'My Profile'. Once you profile pic opens, hover your mouse over your timeline. A 'camera' icon will appear on the top-right side of the timeline image. Click on it and change the timeline pic. You can even change your profile pic from your profile page. Simply click on your profile pic and upload a new picture.