Terrified of child Leukemia

I can’t sleep at night this thought has been running through my mind for a while. I feel so anxious I’m beginning to think I’m being overly paranoid. my son is 3, for the past few months he’s been having lots of bruises appearing on his body - legs, arms, chest, bottom, hip you name it. I took him to the dr a month or so ago and they said he’s just a boy and nothing to worry about. However the past few days he’s started having random nose bleeds so I really thought somethings not right. Should not google symptoms but as you do he’s ticking a few of the boxes and now I’m even more concerned. 
he’s had a cough for 2 years that’s been put down to asthma and takes his inhalers daily with no improvements, he gets a high temperature at least once every two weeks, he’s constantly got infections - recently he had the chicken pox and they even got really badly infected and he needed antibiotics. Family have noticed he’s as white as a ghost and the dark circles under his eyes. I’m really hoping it’s nothing sinister and can be explained. So he’s been referred to the hospital for blood tests after going to the GP again. Anyone ever experienced this and what was the outcome ? 
thanks for reading