Honestly, talking to your GP about it will waste your time more than anything - adult diagnoses are absolutely at the bottom of their priorities, much less actually providing support of any kind.
Far better would be to talk to people who are ND, and see what you have in common. Do some (honest) research on those traits, watch some videos by ND creators, and see where it takes you.
If you still have a strong feeling that you're ND after all of that, you have two options:
#1: Self-identify as ND (whether that's ADHD, autism or something else). Almost nobody will question it, particularly in a professional setting (unless you work in the public sector), and you'll have a decent chance of getting the accommodations you need to be more comfortable. It's totally valid, and most ND people will just welcome you into the tribe and help you with your journey.
#2: Formal diagnosis. For this, you're going to have to go private, unless you want a several-year wait for it.
The advantage of #1 is that it's cheap, but the disadvantage (in my experience) is that if you want to talk about it to anybody, there's at least a 30% chance of getting the, "Oh, you're not diagnosed? So you're not really autistic, then?" response, which is utterly maddening.
#2 solves that problem, but it's expensive - a private assessment usually comes with a £1500+ price tag. Mine was significantly less than that; if you get to that stage and want an assessment but can't stomach the prices...PM me and I'll give you the details.
If I'm honest...being able to talk to people about my particular flavour of autism without them being asshats about it is at least 50% of the reason I paid for an assessment. My other reasons were that while I don't need any support right now, that may not always be the case - and future employers may require formal proof of the condition. I'm also somewhat concerned about care in old age - there's a hell of a gap when it comes to social care for elderly autistic folk. In fact, my wife trains carers, and the modules she's forced to teach on autism are about 20 years behind current knowledge and completely wrong on just about everything.