You could contact your hosting provider and ask if they can upgrade the website for you, however make sure that they create a backup of your website first.
Personally, I would contact your hosting provider and ask them for a backup of all of your files (including database). I would ask for this even if your hosting provider is going to do the backup for you because one day your server may break and you may lose your website data. This has happened to me in the past and I lost my entire website.
Once you have a backup of your files, you can test doing an upgrade on a localhost installation, and then you can run the upgrade on the live website. To upgrade DotNetNuke you do not need access to the database, all you will need to do is upload the upgrade files via FTP over the top of your current DotNetNuke installation files.
For further information on upgrading, this tutorial may be useful, it is for earlier versions of DotNetNuke but the same principles still apply.
How to Upgrade DotNetNuke v3.x to v4.4.1How to backup a live hosted DotNetNuke website and restore it to a localhost installationRegarding image gallery, you may want to look at www.ventrian.com simple gallery module