I was diagnosed privately a few weeks ago because I got desperate as I was struggling so badly at work. I wanted the extra protection of having a formal diagnosis.
Please be aware that GPs cannot diagnose ADHD, it must be a psychiatrist. That includes ruling it out too - they simply aren't qualified to assess whether someone does or doesn't have it. They should agree to refer you to adult ADHD services, but the wait can be years. Some areas don't even have adult ADHD services.
There are a lot of helpful Facebook groups that I would recommend joining. Somewhat ironically, I can't find the names of them right now (!).
If I hadn't needed my diagnosis so desperately, I would have gone down the Right to Choose route (only available if you live in England) which means you have the right to be referred to the service provider of your choice for both physical and mental health issues.
I am not very good at explaining it, but lots of people are using it to access a service provider called Psychiatry UK, as they are commissioned to provide NHS services in some parts of the country which means that you can choose to use them on the NHS if you live anywhere else in England.
I didn't do this but I am hoping my GP will accept a shared care agreement once I am stable on my medication. This means I will have to continue to pay to see my psychiatrist, but my prescriptions can be taken over by the NHS.
I am happy to answer questions too, I am very new to it all myself.