No. The child and dependent care credit is used if you paid someone to take care of your child so you could work. You have not mentioned whether your child has some sort of medical condition which necessitated the extra supervision/help in school, and if that help was recommended by a doctor. The cost *might* be a medical expense that you could enter.
MEDICAL EXPENSES
The medical expense deduction has to meet a rather large threshold before it can affect your return. The amount of medical (including dental, vision, etc.) expenses that will count toward itemization is the amount that is OVER 7.5% of your adjusted gross income. You should only enter the amount that you paid in 2022—do not include any amounts that were covered by insurance or that are still outstanding. Of course, your medical expenses plus your other itemized deductions still have to exceed your standard deduction before you will see a difference in your tax due or refund.
To enter your medical expenses go to Federal>Deductions and Credits>Medical>Medical Expenses
2022 STANDARD DEDUCTION AMOUNTS
SINGLE $12,950 (65 or older + $1750)
MARRIED FILING SEPARATELY $12,950 (65 or older + $1750)
MARRIED FILING JOINTLY $25,900 (65 or older + $1400 per spouse)
HEAD OF HOUSEHOLD $19,400 (65 or older +$1750)
Legally Blind + $1750