Is it normal to feel really ill when first taking celexa (citalopram)?

No. It usually doesn't cause many problems--if you decide it is the Celexa (citalopram) you can try taking a smaller dose with food.
Yes. Yes you might feel ill especially if this medication is not tolerated by you personally. The most common side effect is stomach upset and occasional bowel cramps -these usually decrease over the first week or so as you get used to the medication. But call your doctor if symptoms continue to worsen because you may need to change treatment.