Welcome to Using English.
First, never use "its" for a person unless you're talking about a baby whose sex is known. In fact, the use of the singular "their" for "I don't know the sex or it's an unknown person" is fine for many of those situations.
If you are a female, you would never use "his."
So you can use "her" or you can use "my." It seems odd to refer to yourself in the third person to me. I know you are referring to "a student" but that student is you. I would actually prefer "... that you will find I am a motivated and serious student with great enthusiasm for my work."
I find "thoroughly profound enthusiam" a little over the top.