Among other things, you may be sensitive to:
- frame rate
- strobing or shifting colors
- sensation of movement
- disparity between visual and other sensory input
Depending on your platform and environment you probably don't have much control over these. You can try the following, but as David said you should probably consult with your doctor also.
- Don't play in a dark room - leave a lamp or other soft light on
- Position your chair and screen so that you're sitting comfortably and looking directly ahead at the screen
- Play with whatever visual settings are available to maximize frame rate and minimize visual strobing
- Back up a bit so that the screen doesn't dominate your vision. This has two effects - it minimizes the sensory conflict, and also minimizes your awareness of screen refresh/frame rate
Be picky about which games you play, when you play, how long you'll play, and what you'll put up with.
When you're limiting the number of hours you play, you want to make those hours the best possible experience.
Don't play a game that is dumb or doesn't make you feel awesome.
Don't play when someone else needs your attention. They won't like it, you won't like it, and you won't enjoy the game as much.
If you're playing a multi-player game and can't find the right folks to play with, quit. If your friends aren't online, or you the people you want to play with are already engaged, or the people you find yourself playing with are assholes, quit.
Don't play instead of sleeping. Being well-rested has a big affect on patience, ability to learn, and motivation. Those will, in turn, affect your relationships, school work, quality of parenting, exercise, food choices, etc.
When my second & third kids were born (twins!) I was so very exhausted I couldn't cope. If I got a chance to sleep, I would get woken up 30 minutes later, which sucked. I played games instead, because being engaged in them made me not notice how tired I felt. But of course, this just made the problem worse. Watch out for that.
If I start playing it after a few months of not playing it, my thumbs get sore too. After a few hours I stop playing it and maybe the next day or so when I play again, it hurts less. You might just be needing some rest for your poor thumbs. If you start feeling pain you should definitely give it a rest - don't keep playing until your thumbs literally fall off, right?
You might also want to consider trying out different controllers - there might be a model which has less resistance in the thumbsticks, which would make things easier to move.
In terms of strategy, I noticed that I do try to go for the same patches of clustered objects that are just barely grab-able - this helps me grow the katamari the fastest. Things like sunflowers, desks, and especially trees tend to clump together - once you can get one, you get like 20 in the same area. Same with boats, buildings and the open-sea fishing pens (although if you can get to that size you probably have the hang of it). Fences also seem to help it grow fast but they can get annoying with their odd shapes.
Also, look for things that are actually a collection of inter-touching objects, like a stack of lego-type blocks, or the red mailboxes in the town, or a wall of bricks where each brick is a separate object - you can gain size pretty quickly with those also.