Tests for serious illness are a very stressful time - so I;m really sorry you are going through this - I have been there myself (my own illness)
The only advice I can give probably sounds a bit of a cliche but it is 'one step at a time' and 'deal with what you know'
In other words try to stop you mind wandering to all the what ifs, cope with the information you have as best you can and tell your self you will handle each part of the situation as it changes.
I hope very much that your DDad is Ok, but if he should turn out to have a serious illness, I can say from experience that once you get past the shock of diagnosis, coping in some ways becomes a little easier - you will have a treatment plan and a routine for treatment. You will have practical things you can do to help your parents.
It's the uncertainty and waiting that are especially hard. Try to keep yourself occupied, and make efforts to relax when you can - just a quiet sit down and some deep breathing, or a walk in the fresh air, or listening to your favourite music - anything that helps for you. It will help with that sense of underlying panic and help you recharge your batteries for facing the future challenges.
Things like yoga, meditation, mindfulness etc. can also be helpful. Serious illness is often a long haul - there aren't any overnight fixes. But you can't remain in a state of anxiety and worry continuously - you will end up struggling to function.
So tell yourself 'I know that today this is happening and I will cope in this way (some sort of practical thing or emotional support you can offer your parents and some conscious relaxation for yourself) Then try to keep on an even keel until the next hospital visit arrives. And also never be afraid to ask for help if you need it - it is worth talking to your GP if everything gets too much for you to cope with.
Also I don't know obviously what your Dad is being tested for, but many illnesses have associated charities and helpline where patients and their families can chat to people who will be kind and understanding of what you are all going through, there may even be drop in support centres in your area where you can talk to someone.
That was my way of handling things, of course it's easier said than done, but I hope you can manage to reduce your anxiety a bit, I wish you and your family all the very best x