Aah normal la sayang, I had that too during first trimester, batuk kering mixed with morning sickness is quite common sebab hormones and everything shifting in your body. A few of my mum friends went through the same thing, and honestly what helped us was staying hydrated, sipping warm water or warm lemon water slowly, and avoiding strong smells that trigger the nausea more. But since you're only 7 weeks and want to be extra sure everything's okay, best check with your doctor or midwife la, just to rule out anything else and get proper advice for your specific situation. Take care of yourself!