For you, this job's pretty much about everything between your fingertips and your shoulders. Going through the motions day in and day out can really affect your arm muscles and joints over the course of your career. Carpal tunnel and arthritis aren't fun to deal with in general; imagine choosing between dealing with the pain and not making a living.
It can be a major damper on your work, and you may have to undergo surgery in order to restore your hands to massaging condition once again. And if you're a piano player or video gamer, your thumbs and wrists might not last that long.
At least you won't be alone in your pain. Lots of therapists suffer from these ailments, so if you're seeing massage in your future, be sure that your joints are in decent shape to start. There may be an age ceiling for getting into this career, and it ends around the time you stop being able to move your wrists in a full circle.
There's also the danger present from just touching another person. Working in close enough proximity to sweat on them means that you could contract whatever airborne illness they're carrying. Make sure you wash your hands throughout the day—you want to spread joy to your clients, not bacteria.