Is my judgement correct?

Short answer: Yes.

Let's go through a Fermi estimate. According to Wikipedia there have been only a small handful of Ebola cases in the First World during this outbreak, almost exclusively among people who'd been volunteering in West Africa on missionary or health care assignments. (There has, however, been one case of local transmission in Texas.) Let's be generous and say 20 people with the disease flew in or out of the US over the last month. Now, there are about two million air passengers per day in the US, of which I'm guessing about a quarter are on international flights; that works out to 15 million international passengers over the same month.

Ebola takes close contact to be transmitted; it's not an airborne disease. Since you'll probably be sitting next to each other, that means you'll each only be coming into close contact with one other person on each flight. Let's say that, if they're infectious, that person has a 20% chance of giving you Ebola over the course of the flight (probably an overestimate), and that a case of Ebola in the First World has a 50% chance of killing you. Combined with the ratio of infected travelers we worked out earlier, that means that your chance of dying from Ebola contracted on each leg of the trip is about one in 7.5 million.

That's about as dangerous as driving 30 miles in a car, or a bit less than a mile on a motorbike. And I'm making a number of simplifications that almost certainly inflate the risk: your route for example doesn't go anywhere near West Africa, assuming you're starting near Atlanta as your profile would suggest.

What is it that your family member sees as dangerously increasing the risk of getting Ebola?

• Going to the UK (perhaps they think the UK is likely to be hit worse than wherever you are now)
• Getting on an aeroplane (perhaps they are concerned by being in close proximity to other people)
• Travelling at all (perhaps they want to minimize the number of different people they interact with)

I am far from being an expert and you shouldn't trust me, but my handwavy judgement is the same as yours.

Possibly relevant Sequence article about the availability heuristic.

Don't sweat ebola, for now anyways. There are thousands of cases, trues, but they are highly localized. There have been VERY few western cases. And even if you were on a flight with someone in the narrow window of ebola's contamination stage, you wouldn't be infected with it unless they bit you or you shared drinks or something like that.