In a sense, your GP is right -- this is "your mind playing tricks on you."

Anxiety is "your mind playing tricks on you" in that people who have anxiety tend to over-estimate risk. For example, a person who is anxious about driving over a bridge may act like there's a 50% chance of the bridge falling into the water at any moment. (If that were the case, you would have a big fear about driving over it). But in reality, the odds of the bridge cratering are, say, one in a hundred million. And if your mind estimated that risk accurately, you would have no fear about driving over the bridge, because the risk is so remote. The same is true with your health concern -- your mind "tricks" you into thinking you have a substantial risk of a serious illness -- so you get anxious about it -- while in reality you presumably have no material risk -- as a healthy, young person who has recently visited a doctor and been given a clean bill of health.

Having this sort of health anxiety triggered by your mom's illness is very common. A parent's serious illness is a very traumatic event and it can easily trigger the sort of anxiety you are facing.

The prior poster suggested CBT. That is an excellent idea. CBT is very well suited to this sort of anxiety. It can "teach" you to resist the "tricks" that your mind is playing on you, and to estimate risk more accurately (and then to internalize that accurate risk assessment).