I'm an avid oil painter for years and love the texture of oils over acrylics and watercolours. I stopped using turpentine a while ago not because of cfs but just because they made my house stink really bad. If you are a new oil painter who just starting out, turps probably won't be necessary.
One thing to do is to make sure you have a paint brush cleaner which doesn't have to be turp. There are many chemically safe ones. I have the daler rowney green one. You can even use hand soap if you like but they're not the best for keeping the brushes durable. If you didn't spend much on the brushes hand soap works great.
You can use linseed oil to weaken the paint. Turps can be too hard to use for beginners as I've learned. Turps are only really used for the underpaintings anyway. Fat over lean technique. Most beginner's don't bother with underpaintings because there needs to be specific techniques and so on which can take years to develop. I've only done an underpainting once. Also I'm guessing your using student grade paint?? They will need a bit more linseed but not too much or it will make the paint yellow. Let the paint dry in sunlight too (yellows in the dark) and watch out for dust.
Also last tip. As soon as you get oil paint on fabric wash it of with soap quick! Don't let it dry up. Luckily with oils it takes longer to dry unlike acrylics but with acrylics you can scrape it of sometimes.
I love oils and really hope you don't have to give them up. They are so great to work with if you get the right types of paints without too many chemicals but I think that'd be really hard to find with any student brand of acrylics or oils. If you want anymore tips then say.
