I have visible veins in my palms and fingers, is that normal?

Yes. Without seeing your hands i will tell you it is probably normal. The veins in palm and fingers can be visible/ more visible if you are thin, or have fair skin which is more translucent , or have been exercising , you are hot or excited. There are rare skin conditions where the skin is almost completely translucent and there are rare circulation problems but at 33 years old they are very unlikely.
Check for obstructio. You might need to have this evaluated to make sure there is no blockage in chest - is it one side or both sides?