I have just had a tummy tuck is it normal for my lady parts to be extremely swollen?

Thank you for your question. You should expect to have swelling for three to six months following tummy tuck surgery. It is quite common to have swelling of the vagina. Use of a properly fitted compression garment will help decrease the length and severity of the post-operative swelling. As the swelling decreases, the contour of your abdomen, flanks, and hips will dramatically improve. Please follow your plastic surgeons specific advice regarding your level of physical activity. Hope this helps and good luck with your recovery.

Swelling can persist for several months and will gradually improve and will look better at three months, six months, and even one year. Frequently the pubic area and the scrotal and penis area for men can become very swollen and discolored during the first two weeks due to gravity as this is the lowest area for swelling to accumulate.
While the length of time for post-op swelling can vary from one person to another, it is best to visit your surgeon for an examination if you are concerned or worried about healing progress. Good luck!

There is bound to some swelling of tissues after a tummy tuck procedure, but if there is excess swelling as you describe you need to see your plastic surgeon so that he can assess you for collection of fluid (seroma) and drain it as necessary. 

This is normal at this point in time as swelling is a good indication of healing. Swelling in your pubic area is normal for the first few weeks and it usually takes around 6 months onward for the swelling to fully subside.