My chihuahua pup is in heat, her female part is 3 times normal size, is that normal?

Yes, swelling is normal and will last for several weeks.
As long as there is no green or yellow discharge (indicating an infection)

Bleeding generally only lasts for a week or two, but their entire heat lasts for 21 days.

Keep her away from all male dogs during the 21 days. Once her heat is over it is safe to get her spayed.

You can buy special pants for them to wear to reduce the 'mess' involved, but personally, I just throw some old sheets over the couch and over their beds.
She will probably be feeling a little miserable for the next few weeks, and some girls can get quite clingy... it's all par for the course I'm afraid.