Of course you should accept what she said. If it hasn't, or doesn't change, then you have nothing to worry about. I have a scary mole on my chest that is about the size of a pencil sharpener. It hasn't always been there and I can't remember when it first appeared there. But the only thing I do is check it now and then (but no too often - like once a month or so).
Sixpack has given you amazing advice. In fact, it has even been beneficial to me. You said you know the odds of it being a melanoma are tiny but google made you panic. Therefore, you know from the evidence that it would be better to avoid googling. It is easier said than done. I know because I am often sitting here contemplating whether I should google a new symptom or not. The more you can prevent yourself from googling your symptoms, the easier it will get each time.
This could be your first step in getting over your HA. Just try and prevent yourself with all your might from googling.