Scared so much

I had a chest infection about 5 weeks ago and it took ages to clear. Went to a and E had a chest x-ray and it was normal and so were blood tests. Been back to go as still coughing up white mucus. There was some small black bits and she has done a referral for me to chest team. She told me she is referring me because of my health anxiety and that when I asked her if she was worried she said no and that she would tell me if she was. She also wrote on notes that it's likely to be non sinister. I am still scared to death because I saw the black bits. Can anyone tell me what they think? Also are x-rays good at picking things up?

Thanks in advance.