Everytime I click on my profile picture, skype closes, so I can't open my profile tab.
It's happening since yesterday, and it's very troublesome.
Can you please share the error message from the Windows Event Viewer application log? You can find it by searching for "Event" on the Windows start page.
Windows will show the system application "View event logs" for you. Plesae open that and open the branch for "Windows Logs - Application". Look out for an application error/crash from the Skype app and share the error description.