I have never had morning sickness. The only symptoms I had were tiredness and mood swings. You should still go to the doctor when you can. Until then, try not to stress, because that isn't good for the baby.
Your symptoms fading doesn't mean your baby isn't healthy :-) in fact most symptoms like morning sickness tend to fade around the end of the first trimester/beginning of the second :+) so it's perfectly normal to only be tired :)