No. There is no disease or condition which results in special dependent tax considerations, particularly for a child under 13 [ed]. As they age, they may remain a 'child' for Some tax purposes IF they are certified 'permanently and totally disabled'. For what medical expenses you can deduct (IF you itemize), see https://www.irs.gov/pub/irs-pdf/p502.pdf
So sorry to hear about your child's health problems. There is not any extra tax benefit or deduction to saying that a child under age 13 is disabled on your Federal return. If you have a disabled child over 12 and need to pay for childcare so you can work, saying the child is disabled can enable you to claim the childcare credit. Or if the child is 19 or older, you can still claim the disabled child as your dependent. Otherwise, it does not benefit you to claim that your child is disabled. Your state tax laws may be different.
Of course, any medical expenses you are paying out of pocket should be entered in Medical Expenses in case you have met the threshold for claiming medical expenses as a deduction.
There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.
A child's disability doesn't affect tax filing until he turns 19 (24 if a full time student). Then his disability allows him to continue to be considered a "Qualifying Child" for tax purposes regardless of age. There are no credits or deductions, other than that some items, e.g. special schooling, can be considered medical expenses.
As previously indicated, you may claim day care expenses past age 12. His disability does NOT allow you to claim the child tax credit past age 16.