With a broken arm, a doctor will set it, give you a cast and you will be on the mend in no time. With speech therapy, you need to put in the work in as there is no plaster to apply. This might be where the self-therapy talk is coming in. You can practice on your own and see improvement. A professional will guide your journey, improve your technique and help you move along faster. If you are worried about money, check out the book self therapy for the stutterer by malcolm fraiser. The ebook is free. It gives a path to improve with a bunch of exercises. A lot of therapists in the UK recommend the book so you could start with the book and request sessions on different concepts to help control costs. I would recommend a course or private speech therapy. Like others, it has really helped me.