Can I explicity show tooltip on Mouse Click event in WPF?

No you can't invoked the tooltip on mouseclick. Instead of using Tooltip, you can use Popup control. Invoke the Popup Control on mouse click.

You can force the tool tip to open by setting ToolTip.IsOpen to true. You can get a reference to the ToolTip object by explicitly constructing one when setting the ToolTip property. Instead of

<Image.ToolTip>
    <Grid>
    ...
    </Grid>
</Image.ToolTip>

write

<Image.ToolTip>
    <ToolTip>
        <Grid>
        ...
        </Grid>
    </ToolTip>
</Image.ToolTip>

And then in your MouseUp handler do something like:

((ToolTip)((FrameworkElement)sender).ToolTip).IsOpen = true;