It is very much normal! I was just like that! Everytime I went to an appointment I went there thinking that there would be no heartbeat. Every single appointment! It's a horrible feeling! But you will be alright! Once you start feeling the baby move, your fears will calm a little bit since you will know the baby is fine. Just the other day I became worried because I didn't feel her moving all morning. I was ready to call the doctor and then she started kicking away to remind me that she is still there going strong! So just relax and enjoy your baby! All that stress wont help you any. But word of advice, once the baby starts moving, you have to remember, just like us, there are days when it just wants to hang out and relax so you might not feel it too much. That's normal! =) Try not to go too crazy!
I definitely worried just like that, because I got pregnant a month after a miscarriage. But the best, and hardest, thing to do is try not to stress yourself out too much. I'm keeping you in my thoughts, honey!