Oh please, you're going to give me a swelled head.

Having a swelled head is an expression that means being conceited. Does that help you figure it out?

to figure out what?

To figure out the meaning of the sentence.

You mean she didn´t think it was a good idea that everybody praised her so much. She didn´t want it to go up to her head? Is that what you mean?

Right. Or that's what she's professing, anyway. It's probably one of those times where she says one thing but means another, but it's hard to tell without knowing the character more intimately.

what is your final conclusion then? Do I get the wrong idea, dear?

Kitkattail, your answer did help me figure out what this expression means. I guess she meant all this praise might turn her into a v

I wouldn´t agree. To make such staments you would need to know her character more intimately.

Isn't she just being modest?

Yes, it is not necessary to know more about the character as it is showing her modesty.