I have had 3 babies and I still worried like mad with the 2nd & 3rd, experience didnt make me worry any less!
However, just to reassure you - I didnt get full blown morning sickness symptoms until about 8wks in each pregnancy - they came and went from finding out I was pregnant at 4 weeks up to 8 weeks (eg some days I felt totally fine, others I felt dreadful), then were pretty consistent during weeks 8, 9 and 10, then disappeared again for a few days at a time (getting me all worried), then coming back with a vengeance a few days later.
Dont expect to get symptoms every single day of the week - I certainly didnt, & I have 3 healthy little pickles to show for it. Also, I woke up feeling totally fine most days, but got terrible evening sickness.
Big congrats on your pregnancy - its only natural for you to worry, particularly given you didnt think you'd be able to have kids.
There is worry at each step of the way - once you feel baby kick, you start worrying about regularity of kicks, once you have baby in your arms, you'll worry about whether baby is ok. Its perfectly natural to worry, but just remember to keep the worrying in check - you're pregnant, so do try to enjoy the experience!