Take the medicine. I had a similar experience the other day. This is my first pregnancy and what I thought was regular morning sickness put me in the ER with an IV due to dehydration. I have been diagnosed with HG, am now on Zofran, and trust me, taking medication is much better for you and your baby than dehydration and malnourishment.
It won't hurt your baby, there are reports about some nausea medication that can sometimes cause minor birth defects but they're EXTREMELY rare cases so I wouldn't worry. I had awful morning sickness for 7 months or so and I took zofran, some other medication (forgot the name sorry) when that stopped working, and during labor they gave me the reglan so I wouldn't vomit after every contraction and my daughter is perfectly healthy.
Taking medication during pregnancy is a tricky situation, a lot of women feel uncomfortable about it but getting dehydrated and extremely sick isn't good during pregnancy so your Dr wouldn't give you any medication he thought unnessary. Try not to stress too much (: