Health Insurance Dilemma?

I have an appointment in two weeks to determine the possibility of melanoma and do not yet have health insurance. I had planned to have long-term health insurance in place a month ago, but it has not yet been processed. I want to keep my appointment and just pay for that out of pocket, but am concerned that if I do receive a diagnosis, I will not be able to get insurance after the fact. If I wait for my insurance to come through and wait until August for the next available appointment, can they drop my coverage anyway for only having it for 1-2 months prior to diagnosis? Also, I had a doented incident of Tachycardia two years ago that I was forced to go to the ER for and have been told that would likely rule me out for any short-term coverage options, despite the fact that it does not affect me daily and I do not take medication for it. Oh and I'm early 20s, if that matters. Thanks for any and all help--this insurance situation is stressing me more than the actual appointment!