I think I have a solution for you, a bit tricky though. Do the following

1. Install/enable "devel" module
2. Override page.tpl.php to page--node--%.tpl.php (or you could use the page.tpl.php) 
3. Find the title element in the page.tpl.php , looks like following
 
![enter image description here][1]

4. Make sure that you have a field called icon (note the machine name i.e. field_icon) in your content type 
5. Create a sample of your content type 
6. Click on "Devel" tab and try to find the field_icon or whatever you named the field, as shown in the following screenshots 
![enter image description here][2]


and clicking on the field_icon, you will see a structure similiar to this 
![enter image description here][3]


Just before the h1 tag, in the screenshot of page.tpl.php shown in #3 add a code that looks like the following: 

    <img src="<?php
    	    $var = $page['content']['system_main']['nodes'];
    	    $element; 
    	    foreach($var as $k => $v) {
    		$element = $v ;
    		#obtain the node id, usually first.
    		break; 
    	    }
    	    #$exist = $element[$element['field_icon']['#object']->field_icon['und'][0]['uri'];
    	    if(isset($element['field_icon'])) {
    		print $element['field_icon']['#object']->field_icon['und'][0]['uri']; 
    	    } else {
    		#does not exist
    	    }
    	?> " />


The code above creates an image tag, and its src value would be the value of the URI of the icon. Use Devel (or kpr($page['content']['system_main']['nodes']); inside page.tpl.php) tab to figure out what to replace with $page['content']['system_main']['nodes'], probably it might remain the same for you as well.  

Once you got the content of the $page['content']['system_main']['nodes'] or similar then loop through it to find the node-id (which can be anything). The reason I have a break in loop is because, I am interested in first element which is node-id, see below

![enter image description here][4]

And finally access the URI as shown in the following Devel Screenshot

![enter image description here][5]


Nothing will be printed in pages where there is no field_icon (i.e. icon machine name), and the icon should be printed in pages that have that field in its $page variable. Good luck. 

  [1]: https://i.sstatic.net/6l3Fb.png
  [2]: https://i.sstatic.net/XPe2F.png
  [3]: https://i.sstatic.net/zgEN8.png
  [4]: https://i.sstatic.net/Z5sxh.png
  [5]: https://i.sstatic.net/EocS8.png