I think it really depends on a case by case basis, because each individual is different.
When I was struggling severely with intrusive thoughts between the ages of 16-17, I definitely needed a professional to guide me through because I had little knowledge of the beast. But for my most recent struggle with emetophobia, I have been able to tackle that on my own through self-taught education on the root of anxiety, and deep breathing. I would highly recommend a book called "Rewire Your Anxious Brain".
People who struggle with anxiety (including myself sometimes) often give the anxiety way more credit than they give themselves. It is a terrifying beast sometimes, but once you unravel the root of it, it's honestly a lot more manageable.
If you are unable to see a therapist, I don't think it would hurt to do so by yourself. Take small steps though, and feel free to PM me if you have any questions.