Hi,
Don't worry, all will happen good. Well, when I was young and a couple of years ago, my nose used to bleed sometimes. But that doesn't mean that he will or has Thalassemia Major. It can depend on multiple factors, also the heat in your country or area; as a side note India is also very hot climate country and so I resulted in nose bleeding couple of years ago but now I don't have it.
About him being thin, haha, my brother (4 years older than me) was only around 1 or 1.5 kgs during born, doctors were saying he might die as well, because the normal weight should be around 3 kgs or so, he was also weak. But as he grew, he is now solid as a rock. Having a stature of 5.9 foot in height, good muscle mass and perfectly normal.
Don't worry, all shall happen great. I don't advise you not to read more about this, definitely read or research more about it till test results come, but don't engage your mind more deeper into this and feel bad. The more you think, the more you'll be stressed. Same is with me sometimes, I develop a phobia when I go on reading more and more and end up concluding that I may have this disease, as well.
May god bless you and your son and give your family enough strength. Keep us updated on lab result.
-Pratik.