Ok, it seems like you've already gotten a ton of advice, and I fully support telling your OB &/or midwife. Tell them EVERYTHING!
I know everyone says Zofran is safe, but do you really think nature intended us to take pharmaceuticals for a natural process? It's more likely that your body is trying to tell you you're either 1) getting or 2) not getting certain nutrients that's causing such a reaction. I'm 26 wks pg right now & had horrible AM sickness til about 18 wks. Some things I didn't learn until farther along...
For instance, I recently read that studies show pg women who get TOO much iron have a higher incidence of pre-term labor, whereas those who had a smaller amt went full term.
It seems that once we're pg, our bodies do a BETTER JOB of absorbing IRON from our foods, and when we take prenatals with high iron supplements, we're getting EVEN MORE IRON than if we weren't pg. My prenatal has 4 tabs to get a full-dose, but this gave me 333% iron. I finally started taking only 2 in AM & 2 in PM, but often times I couldn't stand taking the second 2.
Instead I starting taking only 1/2 prenatal plus full B-complex & my AM sickness went away.
You can also gauge if you're getting too much by whether or not you want high-iron foods. Do you CRAVE chocolate or does the thought make you nauseous? Dark chocolate (70% or higher) has a high iron content (part of what makes it so good for us).
Also, you mentioned trying hard to eat fruits & veggies - DON'T! You body has a good store of nutrients built up from how you were eating right before pg. Your baby is telling you what nutrients s/he needs right now. If you want ice cream, eat it!!! Others have already said this, but eat in small meals all thru the day, even at night if you need. You need to keep up metabolism, and prevent yourself from ever getting too full or too hungry.
As for ginger, definitely do it. But don't waste money on pricey supplements! Buy a piece of ginger root (it will cost about $0.30 depending on size & that's for organic!)
Boil a cup of hot water. Grate the ginger with the small side of cheese grater & put into a tea ball (or straight into water if you don't have one). Cover & steep for about 5 mins. Add a tsp of honey or agave nectar, a drop of lemon or lime juice & a sprinkle of SEA SALT (not plain table salt!). Keep the ginger in the water. Drink! This is esp nice to drink in the middle of the night & 1st thing in AM. If you don't drink it all, just keep & reheat later.
The ginger will help with nauseousness, the hot water provides ionized water which is REALLY good for you, the honey or agave make it sweet & easier to drink, plus the minor sugar content helps your body absorb water faster, the lemon or lime will also help with queasiness & provides a small amt of vitamin C, and the sea salt provides essential trace minerals and provides for electrolytes. You don't need to buy Gatorade when you can make this for pennies! Using these things to help your body absorb water is also really important so you don't get dehydrated.
Also, I highly advise drinking a "Pregnancy Tea" - Yogi teas makes one, I can't remember name of other off hand, Natural something or other. It contains things like Red Raspberry leaf, spearmint, stinging nettles, etc. If you only drink as advised, you will be in great shape! These herbs help firm up your uterus and prepare your body for delivery. I recommend seeing an herbalist (only need to go once) & she can advise you on customizing blend for your body. I saw Liz Johnson at Magus herbs ###-###-####) - she specializes in herbs for pg. At 9 wks, prior to seeing her I had a subchorionic hemorrhage (bleeding). After this, I started taking pg teas, then I found her, supplemented with more nettle & partridge berry vine, and at my 18 wk ultrasound, the hemorrhage was COMPLETELY gone. She charges $60 for 1 hour, but gives you tons of info customized for you, and is available for free for any follow-up questions thru-out pg. And of course, make sure to tell your doctor if you take herbs, what they are, and never take more than they tell you to. My midwife is fine with it, esp. seeing the results so far.
Good luck & congratulations!!!