What to do after a diagnosis is NOT confirmed after an assessment?

I really feel for you.  That sounds so incredibly frustrating, after such a long wait.  We all hope that we'll be listened to and validated.  
Can you contact the person who assessed you and have a dialogue with them, telling them what you've said here, and making an appeal about the result?  I've read on this forum about at least one situation where a person emailed the assessor afterwards, and their diagnosis was updated.

If you don't get any success this way, if I were you I would look into options for a second opinion from somewhere else.

I do not think that speech delay is at all a requirement for diagnosis. Back in the day, 'high functioning autism' was differentiated from Asperger's on the sole grounds that the former had speech delay and the latter did not. If you accept the social model of disability, then the presentation of any traits as being disabling is entirely dependant on the environment that the individual experiences. As an only child with three doting adults, my grandmother lived with us, my life up to school age was not presenting me with any challenges that I could not cope with. I probably did exhibit quirks connected with my autism, but they would not have been particularly noticeable. This changed at four and a half years of age when I went to infant school, and in response to this more challenging environment I became selectively mute. I was entirely mute for 3 months and following this had shorter episodes of mutism throughout my infant school life.

Not true. I had no speech delay. In fact, I was talking ‘like an adult’ before I was even at nursery school.

OK, I haven’t been assessed yet, but the same was true for my daughter, she had no speech delay.

Not everyone has sensory issues or meltdown, so how can one differentiate a childhood temper tantrum with a meltdown? Hindsight is a wonderful thing, and many of us cannot see what was true in the past without it.

Did you list all your problems? Do you feel you have some of the traits? What’s your gut feeling?

How do you know that you felt it didn’t affect your life much if you didn’t know you were (Possibly) on the spectrum?

I think your diagnosis of sorts is questionable. It isn’t helpful either. We know that Autism can look like a lot of other disorders.

You are entitled to a second opinion, just as you can go private.

This isn't always true of girls though as we learn to mask, even subconsciously. I always just thought I was shy and emotional, as did everyone else. Women then struggle to keep up this masking in adulthood, hence why so many of us are experiencing late diagnosis. 

Autism is a developmental condition and regardless of whether you had an idyllic childhood or a traumatic childhood there must have been some speech delay (or disorder), cognitive differences or sensory difficulties present throughout your childhood if you are autistic. 

Speech delays (and speech disorders or communication difficulties of some form), or learning difficulties are hallmark signs of autism spectrum disorder. Those referred to formerly as 'High functioning' autistic children may be much more socially inclined compared to those with more severe autism, however, the same communication issue applies to all those on the autism spectrum. Autism doesn't appear suddenly at puberty. And as debilitating as anxiety is, it is a symptom of the difficulties that autistic people encounter in the environment, but it's not an autistic trait in itself. 

There are studies that indicate that some autistic people cope better in adulthood, but I have not seen any research that suggests the opposite to be the case. It can happen that older generations are not identified in childhood, but even so, they/we do still all have difficulties in childhood—which are often put down to other conditions.

If you don't feel that you were affected in your early life then it's difficult to see how you could be autistic. If your difficulties only began in adulthood then I would guess he is right and you should probably go for a mental health assessment as its more likely to be some other disorder that's emerged and needs to be addressed.

My life became increasingly difficult the older I got, so I don't know if I agree with what they have said to you. They expect us all to be bullied, and indeed I was, but I'm not sure it's fair to assume every autistic person will be singled out or excluded. Other kids CAN be accepting of other children, even the stranger kids. Kids don't have much else to struggle with if they have a loving family either, so we are a bit more limited in childhood but as adults we usually take on a lot more responsibilities and more is expected of us. From my mid-teens onwards I struggled more and more. I couldn't rely on my natural intelligence and I needed to focus and also navigate more social situations to succeed, and sadly I couldn't.