Question: This main character was genetically created by an alien species.

This particular alien specie are highly intelligent and have numerous abilities such as telepathy, defensive powers similar to magic and can change/morph into any living thing. I wanted to add a certain twist to my main character that makes her different than aliens but have something about her that could change or transition like the alien kind could do.

Before deciding on an ability, I wanted to see if this is even possible for the specie to genetically modify and create her to do this.

Answer: 
The idea of a [human-alien hybrid](http://tvtropes.org/pmwiki/pmwiki.php/Main/HalfHumanHybrid) takes you far beyond scientific plausibility, so "genetically" and "possible" don't really apply.

* [Mules](https://en.wikipedia.org/wiki/Mule) are hybrids between horses and donkeys, and they're sterile. That's despite the fact that horses and donkeys are from the same kingdom, phylom, class, order, family and genus.
* Same for most [Ligers](https://en.wikipedia.org/wiki/Liger).

You can't even be sure that the aliens use the same amino acids or the same [chirality](http://tvtropes.org/pmwiki/pmwiki.php/Main/MirrorChemistry). So you're left with the *magic* explanation unless you're prepared to fiddle with the evolutionary history of Earth.
It sounds like eyes changing with moods is the least of your problems with plausibility. Magic and telepathy already put this story solidly in the realm of fantasy rather than science fiction, so you don't need a scientific explanation.

However, if you want a scientifically plausible creature whose eyes change color rapidly (regardless of the trigger), I would recommend them having chromatophores in their irises. Chromatophores are the kind of cells that allow cephalopods such as octopus, squid and cuttlefish to change color, and they can change at a moment's notice.