Why do I freak out when my children are sick or simply if their leg hurts I panic and think they might have leukemia, I google symptoms all the time?

Hard to say. This may be a form of displacement. You pursue a line of investigation that gives you "good mother" points instead of addressing issues that trouble you. You may want to find a therapist and discuss some of your fears and develop ways to address them .It in not uncommon and you can find help. You have done the first thing by realizing something feels wrong.
Health anxiety. can manifest in fears that we have a major illness triggered by mild or non-existent symptoms. It can also be projected on to our loved ones. Please see a mental health professional who can diagnose POSSIBLE anxiety disorder and help you. If medication is offered please don't stop there. A therapist can teach you specific strategies to help, which is what is needed. Peace and good health.
Anxiety. You seem to be very anxious. Consider meeting often with the pediatrician about these concerns. He/She might be able to reassure you about your concerns. It always helps to hear it from the professional sometimes.