OP, don't worry.
In fact I think there are many people who claim, rightfully, DLA or PIP and also get Carers' Allowance - I'd go chat to the CAB and/or a local Disability Rights Group and get help with the forms and they will advise you not to worry.
I used to work for a helpline where we helped parents with DLA forms (and ran a large local group of parents of kids with a similar disability) and held many hands through the old DLA process. I recall quite a few parents on DLA for one reason - and none of them had any SS involvement.
In any case, the SS don't even come out for kids who are in danger, being abused, etc (understaffed) so they don't have time for involvement in this.
My husband is in the process of applying for PIP (He has dyspraxia and is deaf aloong with some oher problems) and if he gets it, I will claim Carer's Allowance for him, which means he - the disabled adult in the family - will be claiming Carer's Allowance for our son. From what I can see online there is no contradiction there, as many disabled people will care for a disabled child. I'd have no hesitation to claim what is your's.
One of my sons is autistic, was diagnosed at the age your child is and got DLA not long after. This was an award "For Life" so we never had to worry about it again until it was changed to PIP this year. Now mysteriously, his autism will vanish in 5 years as his award is only for 5 years!
Children still get DLA not the punitive, harsh, elusive PIP - so you won't be put through the nightmare of a PIP application (my son's change from DLA to PIP was probably the most traumatic 6 months of my life - even counting his original diagnosis). DLA is much more humane to the claimant and much more sensible (and accurate).
I would however enlist help. I got brilliant help at a local Disabled Rights Group - free to me because they're Lottery funded and if we had have to go to appeal, they'd only fight t for you if you use them to help with with the initial application forms. And if they are behind you, the majority of claimants with support from CAB or a Disability Rights group do go on to get an award.
So please don't do this alone.
They will also answer ALL your questions and from a knowledge of current law, and current experience on the ground in your area.