Sorry, SLT = Speech and Language Therapist which isn't only for language, it's for things like chewing, swallowing and a fair few other things.
Diagnosis is a strange system, in my area a Paed can diagnose Dyspraxia but an OT can only diagnose Sensory Integration which for the balance/co-ordination stuff from a Mum point of view, there's only a whisker between them, but Sensory Integration is not recognised as a disability.
A SLT can diagnose pragmatic language difficulties, processing speed, communication difficulties and other stuff, (not a disability if they do though, it's a Significant Language Impairment) but an Ed Psych can diagnose ASD which is a disability, again for the communication bits from a Mum point of view is particularly similar.
Also one professional will not contradict another. This is why the Team approach works so well, all of the professionals share the test results, observations and conclusions and come to a joint decision on diagnosis or main diagnosis (dx) with co-morbids.
However, it depends whether the team approach is available or whether you have to keep pushing for one professional's opinion, then another, then another. Or go private, but then some Local Authorities won't "believe" any diagnosis or implement any interventions unless the practitioner is an NHS one.
Sometimes, you can find a practitioner who works one day a week for the NHS and the other four as a private doctor, which means the Local Authority have to "believe" what they say, whether you pay for their services or use the NHS route.
The Dr. who dxd my relative as an adult with ASC worked like that, but I was never told about it or given the option to see them privately. I would have done as it was over an 18 month waiting list for an NHS dx from that Dr.
My relative is now in their mid-twenties, so some of my information may be out of date, but that's how the diagnostic pathway has been for us.
Schools should put interventions into place based on a child's needs, very often this doesn't happen without dx because schools have to apply for funding and it seems that SENCO and some professionals like to adopt a wait and see approach. again, a lot of it is postcode lottery.
Getting a child's extra needs identified and getting help for a child who has extra needs really shouldn't be this difficult, but mostly it is.
You'll get there, but be prepared for a bumpy journey, these boards are a mine of information, no matter what you're trying to battle through, someone can point you in the right direction.
Never give up 