Is 'add insult to injury' a harsh expression?

I work at a hotel. I sent a cheaper booking quote to a lady and she paid the amount specified.

Afterwards, upon contacting her, she refused to pay the original correct amount and demanded a stay. To add insult to injury, she has cancer and needd to stay in a bigger room.

Is this a harsh idiomatic expression?

English is my second language and my boss is a native Australian (he's living here in Brazil), I suppose by explaining this to him in this way might look very harsh.

The meaning of "add insult to injury" in the Cambridge Dictionary is:

said when you feel that someone has made a bad situation worse by doing something else to upset you

The way it might be used in your situation would be:

She's suffering from cancer, and to add insult to injury we increased the price of her hotel room.

A phrase that might be more appropriate regarding the bigger room would be "to make matters worse":

Not only did we quote her the wrong price, but to make matters worse she has cancer and needs a bigger room.

Without understanding exactly what your disagreement is about, I'd suggest, "To aggravate the situation...."