Sure you can.
If you have created a myCloud account from webmail you can use it to store all your pictures and file also indipendently from bluewin.
To see all that you can do with myCloud we recommend that you start by logging into myCloud.ch
Please be sure you give your Swisscom login credential to log in (the same you use to login into bluewin)!
You can also download the mobile apps for Android from Google Play or the app for iPhone/iPad from the Apple Store and start uploading all your pictures automatically into myCloud.
With the myCloudSync client you can also keep your important files in sync among your computers and myCloud.