Generally speaking your hCG levels peak at 10-12 weeks, although for some women they peak a bit later or earlier. After that they start to slowly decrease to a degree, which is why some women will start to feel better after the peak and subsequent drop in hCG levels. However, for some women the levels may peak and then never drop much. Even more so the 9-12 week average hCG levels can be anywhere from 25,700-288,000mIU/ml, which is a huge range and in theory really high numbers may make a woman more sick, or she may just be more sensitive. Every pregnancy is so different too. With both of my boys if I had ms I don't remember it, so I don't think I ever did. With this one it's been horrible to where I can't function most of the time without Zofran.
In short, yes it's very normal to not start feeling sick until later in pregnancy. There is nothing wrong with requesting anti-nausea meds for ms. There's no reason to be miserable when you don't have to. Zofran hasn't been a cure all magic pill for me like some women, but it does usually help quite a bit. Hang in there! Hope you start feeling better soon!