Hi D.! I'm due with my first in June also! June 12th to be exact.
I am also on Iron (for anemia), prenatal, and I was just diagnosed last week with gestational diabetes. Sounds like you were tested for that and you are not. What I would do is call your doctor just to make sure everything is OK as far as your swelling. I know that we are going to be retaining water, but we also haven't been through this and are concerned when something like this happens and do not know what is the right amount of swelling, etc.! :)
I did work with a girl that started getting puffy in places like her fingers, feet, face, etc. and hers was actually the start of preeclampsia (high blood pressure). She had to be monitored more closely...stay off her feet...she was fine...and had the baby a few weeks ago and is home with her little girl doing very well!
I think where people get in trouble is when they feel like they are bugging the Dr. or calling too much. If we ignore our issues or concerns then that is not good for us or the baby...that is why they get paid the amount they do to deal with us crazy hormonal pregnant people!! :)
Just call to put your mind at ease about the swelling and the cold. The other stuff you (and I) are taking are just vitamins so don't worry about those.
Good luck!