Actually you have the makings of a good story there. That's because your "characters" are acting a little "out of character" for who they're supposed to be.
As one of the commenters pointed out, a knight is a member of the nobility. Not quite "royalty" but not far from. And ordinarily someone who would not be intimidated by a princess, because he is "milord" himself. That is, someone who is rich himself, but not quite as rich as say, Ivanka Trump (who may become "first daughter or "princess" if her father is elected President).
Thus, the knight shouldn't lack things to say, because they will be prescribe by royalty etiquette. A "safe" subject is weather. He might say something like, "It's a nice day, Your Highness." The conversation could get awkward when it gets "personal." But that's not limited to knights and princesses.
The princess is an unusual one, because she is willing to look past the knight's "status" to who he really is. Most princesses aren't that way, because they expect to be queens someday; the classic counterexample is Marie Antoinette, who was a princess before she became Queen of France.
Your knight is a perfect foil. He is not an "opportunist" who wants to capitalize on the princess' status. And he's got a viable alternative in his own sweetheart. That's why the princess wants him for all the right reasons. The prince has a choice to make. He's clearly comfortable with his sweetheart and uncomfortable with the princess.
How will he make his choice? Will the sweetheart "fall down" and the princess come through? Will there be a "national emergency" that goes beyond the personal emergency of the knight saving the princess' life and will that help define the knight's choice? That was the plot of Aida. If the knight elects the sweetheart and not the princess, will that be a tragedy, or will she go about her business of finding another one?
There is also a potential conflict because the princess is "chasing," dating, and potentially marrying "beneath" her. What do the laws of the kingdom say? Do they forbid her to date "knights?" Do they allow her to marry a knight, but she will have to forfeit her role as princess to become a knight's wife? Will she be happier if she does this? Or do they allow her to raise him to her level?
In real life, the Crown Princess of Sweden married her gym trainer, that is a "knight." He will get to be called Prince," but when her father dies, she will become "Queen" and he will remain a prince and not a king.