Is it possible to correct my hollow eyes that (kind of) stick out from their orbit? (Photo)

You do have a deep fold of your upper lids.  But overall your eyes are quite beautiful and you do not need anything done for them.  You are too young and I think your eyes look nice.

There are two issues here.  From the pictures, it appears that you have ptosis, a condition where the upper eyelid margin/border sits low on the eyeball/globe/iris.  The other is what can be called a negative vector, whereby the eye sits further forward in the eye socket, creating a hollow.  The ptosis can be addressed with a surgical procedure.  The hollowness under the eye can be addressed with a filler such as Belotero, Restylane, or free fat from your own body.Be sure to consult with a doctor with a lot of experience with these techniques.Best of luck!

This makes your eyes look heavy.  With retraction of the levator aponeurosis, this can sometimes take some of the orbital fat with it making the upper eyelid look very hollow.  Repairing the ptosis can sometimes (but not always) also help make the upper eyelid look more full.  Be careful who you see.  You are looking for a fellowship trained oculoplastic surgeon who is board certified in ophthalmology.  The American Society for Ophthalmic Plastic and Reconstructive Surgery maintains an international directory on their website (URL listed below).  This can help you find a well qualified surgeon close to home.  

There is some hollowness around your eyes. However, this is not making your eyes look tired and sleepy. You have a condition called ptosis which can be improved with upper eyelid surgery. It involves surgery to reposition the levator muscle so that your eyes will look brighter and more open. Consult with plastic surgeons in your local area who know how to perform this surgery well. Thank you for sharing your question and photos. Best wishes.