Should I be worried if my morning sickness stops suddenly?

No,but. Do talk to your ob. Why. You are at the lower cusp of when perimenopausal needs to be considered. Considered! not alarmed. A call to your OB is in order. Best wishes.
No. Nausea and vomiting of pregnancy symptoms usually peaks at 8 weeks and most often gets better by 16 weeks. This may be normal for you depending on how far along you are. If you start spotting/vaginal bleeding, you should call your doctor or midwife.