Medicines during pregnancy are not to be taken lightly, but in certain instances, the benefits outweigh the risk. Zofran works, but like all drugs, it can cause negative side effects; and one study recently highlighted a potential problem with people who have underlying heart problems, so I'd recommend getting yourself checked out to rule that out before taking it.
One of my friends has HG (hyperemesis gravidarum -- "really bad pregnancy sickness") and has to take Zofran and other things during pregnancy to keep any food or liquid down and keep out of the hospital; however, in this current pregnancy (her 3rd), she happened to discover that her nausea and vomiting were more manageable than in her other pregnancies, and it seemed to be linked to her following a very low-carb diet. She happened to read about that between pregnancies, so went on this diet as soon as she even thought she was pregnant (i.e., as soon as her nausea started -- even before her period was late!), and discovered that as she strayed from the diet, her nausea and/or vomiting increased, but if she stayed on it, it was manageable with just a few medications. It seemed to be related to her blood sugar levels, and even good things like fruit and whole grains would upset her levels and cause a high followed by a low, and make her sick.
Anyway, you may want to try a very low-carb diet, just to see if it helps.