Yesterday while out on my daily exercise (I live in London) I had to cycle through a pothole (bus too close behind so couldn't swerve or stop) that jolted the whole bike. I then noticed a rattling sound from the bike on the rest of the ride, although it seemed to be handling normally (gears, steering, brakes). Nothing is obviously loose. Given that there aren't any open cycle shops near us, is there any way to check what is damaged on the bike with limited tools and experience? Will it be safe to continue cycling on? The bike is a Trek Domane SL 5 2019.
CFC frames are not as fragile as many people seem to think they are. If you got a heavy jolt but didn't feel like you were going to be thrown off the frame is probably fine. I'd be more immediately concerned about the wheels than the frame, and that may be the source of the rattle.
You can examine the frame closely looking for cracks. If it's dirty clean it first. Using a bright light will help.
Is the rattle coming from the drive train? Does it happen when pedalling only? Does it happen when coasting? Or does it happen when you go over a bump and seems to be something loose on the bike? If the latter, a good way to track it down is to pick the bike up and bounce it on the ground fairly hard on it's tires. By carefully listening you can track the noise down. Trying to locate a source of a rattling noise is almost impossible when actually riding.
Check your wheels are running true. Check spoke tension by systematically going around the wheel pinching pairs of spokes. You may have a spoke broken at the nipple end that is hanging on in the rim.
It's a good idea to learn some bump-mitigation techniques. for smaller bumps raise your butt off of the seat, keep your knees bent and absorb some of the impact. For bigger bumps it's useful to know how to pull off even a small bunny-hop.