Hi mama! Am also working in healthcare and currently week 18. Am thalasemic so on iron pills too. But iron pills will take a while to get your anemia controlled, from a month to a few months.
Have you been eating oily foods? Try to have meals on time (less oil, less spicy) and drink your fluids! Dry crackers help with nausea, at least for me!
Stay healthy and keep going! And do let your gynae know of your concerns in puking. They might be able to prescribe meds if they get serious!