You probably know that the way to getting rid of phobias is gradual exposure. That's what CBT (cognitive behavioral therapy) is about.
I have great difficulty handling blood and needles (as in syringes). Even when shown on TV I look away. 🙂 Recently I began watching the British TV series Critical. It probably contains as much blood, scalpels, needles, and human internals as I have ever seen. I started by looking away much of the time in the first five or six episodes. Then, gradually it got a little easier to see more of the "problematic" parts. At the end of the first season (episode 13), I could watch the whole episode without too much discomfort and I even got a bit curious about the procedures.
This is a huge improvement. I am not sure if it has affected my ability to look at blood and syringes in real life.