profilePhoto.css

.parent{
	position: relative;	
	display: inline;
}

.linkme{
	position: absolute;
	bottom: 0;
	right: 0;
	opacity: 0;
	visibility: hidden;
}

.linkme img {
	width: 200px;
	height: 100px;
}

.background{
	display:inline-block;
}

.parent:hover .linkme{
	opacity: 1;
	visibility: visible;
}

profilePhoto.html

<div class="parent">
	<a class="background">
		<img src="https://media1.popsugar-assets.com/files/thumbor/mycOrIvY8rgt24INHoUOskGXIpk/fit-in/2048xorig/filters:format_auto-!!-:strip_icc-!!-/2014/09/19/978/n/1922507/3a1a55fda9cc796d_thumb_temp_image13465311411161397/i/Funny-Cat-Costumes.jpg"/>
	</a>	
	<a class="linkme" href="http://www.mayashavin.com" target="_blank">
	 	<img src="http://cdn.boilerroom.tv/wp-content/uploads/2014/08/cute.jpg?7c4b8e" class="child-photo" />
	</a>
</div>