No drug is technically "safe" in pregnancy as drug companies can't do proper trials in pregnant women. Most drugs that are prescribed are tested in pregnant animals, have no forseable pharmacological effects that could harm a growing fetus, and have few or no reported complications/reactions when initially prescribed to pregnant patients.
This is reflected in the "cascade" or order of prescription of drugs, which is based on 1. risk of side effects, 2. cost to the NHS (and 3. the doctors familiarity/preference for prescribing said drug).
For Hyperemesis, the cascade is usually as follows (according to my Gynaecology Regristrar Friend)...promethazine, cyclizine, prochlorperazine (Stemetil/Buccastem is the trade name), metoclopramide, domperidone, and lastly ondansteron/ondansetron - these are all the actual drug names, they may have different trade names.
No one can be 100% sure that these drugs will definitely not cause any problems to your baby ? BUT ? what will definitely cause a problem is UNTREATED DEHDRATION and ion imbalances, not only for your baby but also for you.
Your doctor will test you for dehydration based on your blood pressure, heart rate, and the levels of KETONES in your urine.
I had Hyperemesis from week 5 and a half to week 10/11 and was hospitalized and put on a drip 3 times and given all of the above drugs (the only one which stopped the vomiting was Ondansteron?. until the next bout of vomiting!), and last week I had my nuchal and dating scan. On the scan was a very healthy looking fetus waving its arms and legs, with perfectly developed spinal cord (despite me not keeping down folic acid for weeks), nasal bones, heart and other organs.
I still feel nauseous and knackered all the time and occasionally have days where I vomit 2/3 times and can?t eat anything but I?m a lot better than I was.