You necessarily need to write off career paths because of RSI. And keep in mind that whatever else you go to is likely to have its own set of physical detriments! Certainly some jobs are way more prone to particular injuries than others, but with proper control measures in place, you vastly reduce the risk of recurrence. I suggest you get yourself to a physiotherapist, ideally a specialist in the body parts you're getting the pain, and see if there are adjustments you can make to your working practice to keep your current choice of work open to you.
If it's typing/mousing related pain in your hands, wrists etc, there are arm exercises you can do to free up the impinged nerves and correct dodgy posture. And the physio will be able to advise on desk and chair set-up, and modified equipment that supports your hands and upper body in a neutral position. For example, I have colleagues who use upright computer mice, and others who use a kind of joystick mouse, both of which keep hands and forearms in the neutral "thumbs up, palms facing in" position. I use a trackball mouse, and have my keyboard blue tacked on the desk close to my body, to prevent me overextending my arms/shoulders.
I know it's harder for temp workers to ask for adjustments, but your employer(s) still has a responsibility to look after your H&S, and a lot of the "adjustments" are things they should be doing anyway: providing properly adjustable workstations AND training staff how to use them; Encouraging short, frequent breaks from repetitive tasks, etc... But if, for example, you find a mouse and keyboard that work well for you, buy them and take them with you to each job.
By the way, if it can be clearly demonstrated that your injury is caused by the work you do, you might have a claim against the employer. If you're a member of a union, talk to your H&S rep. It needn't become litigious, but sometimes it's not that obvious to employers that a few, often cheap, adjustments to working practice on their part will contribute to a healthier, and therefore more productive workforce.