Yes, both you and your ex can claim the child care expenses you each paid. If you are a single parent, they should be automatically populated to your return.
If you are filing as married or common-law, you will need to make sure you have entered your new spouse's income as well. If you haven’t entered your spouse’s income yet, TurboTax assumes your spouse’s income is zero and transfers childcare expenses to them. Also if your new spouse does have a lower income than you, he/she will have to claim for the childcare, even though he/she may not have paid the expense.
More reasons why the childcare expenses may not be calculating can be found here: