Lucy, confidence comes from being on boats repeatedly, and finding out with your ears and eyes and hands (and butt[g]) just what the boat may do. FEAR IS A GOOD THING. It prevents us from doing silly things like petting the sharks.
What you are fearing is the unknown--and that's normal. After you have been out a couple of dozen times, with sailors that you have some trust in, you will find out that it feels normal to walk "up the walls" in the cabin when the boat is heeled.
On the rational side of things, it is really really hard to capsize most keelboats. They are designed so that they will tip a certain amount very quickly (typically 10-30 degrees) and at that point, the opposing pull of the keel (big lead weight, remember) overcomes the wind pushing against the sails--because the sails are now angled over and the wind is spilling off them madly, instead of pushing them over.
In technical terms, boat designers talk about "form stability" versus "dynamic stability". A boat with good form stability would be like a raft--you can't tip it over without really getting one side up high. Faster boats, racing boats, usually push more for dynamic stability: Like a bicycle, they "stay up" best when they are moving. When you first step aboard one, it will be very tipsy. As it comes up to speed and balance (at a designed heel angle, not flat) it will become much harder to tip.
If the boat makes you nervous, there's also nothing wrong with taking a benadryl or sominex (mild antihistamines that have a sedative effect, sold on the counters in drugstores no rx needed) to take a little of the edge off.
If I had gone sailing in what I call "a good blow" in the first season that I learned to sail....I'd have never gone back. Now? "Wheeee!" And logic has nothing to do with it, I've just learned that good boats, in good hands, are damned robust creations.
So find people you can trust, push your edge a little, and remember the Kenyan proverb about how to eat an elephant: One bite at a time.[g]