If you run the PowerShell cmdlet Get-AzureVMImage , you will see all the images. As pointed out by @Gaurav, those that correlate with My Images are named Publisher User . So, again, using PowerShell, here's how to see only your images piped to Where-Object :
Get-AzureVMImage | Where-Object { $_.PublisherName -eq 'User' }
If you want to see the image names in the console, you can send it to ForEach-Object :
Get-AzureVMImage | Where-Object { $_.PublisherName -eq 'User' } | ForEach-Object { Write-Host $_.ImageName }
Note: If your PublisherName image is empty, use Category -eq 'User' instead.
Here is an example of output from my subscription:

EDIT If you use the CLI for Mac / Linux, you can run a slightly different command:
azure vm image list
Or to return json:
azure vm image list --json
Once you have json, you can, for example, plug in a command line tool like jsontool to get your own image names (the image name is returned in the Name key):
azure vm image list --json | json -a -c 'this.Category == "User"' Name
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