My daughter wheezes when playing sport & is now sick and wheezing and chesty. i used to have asthma as a child, is it likely she has? can gp diagnose?

Yes/yes: Asthma is a variable spectrum with some so mild they never knowing they have it to those who depend on daily meds to survive. It is heavily influenced by genetic inheritance with different forms within the same family. Exercise induced bronchospasm is part of that spectrum. Any primary care doc with enough experience can verify this or send you where you need to go for testing.