Is there any program American can take advantage of to help offset childcare costs during Covid-19?

Some employers have waived some open enrollment deadlines for applying for a Dependent Care Inflexible Savings Account (a "DC FSA"). This is implemented as a deduction from your income, that can be spent using pre-tax dollars. For 2020 and 2021 the limit is $5000.

For more see https://www.investopedia.com/articles/pf/09/dependent-care-fsa.asp

If you still can, get on board for 2021, however keep in mind unspent dollars get donated to your company.

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Look into the "Child and dependent care credit". Note that age limits are waived, depending on the disability of the child. And there are phaseouts depending on your income.

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And note you can't stack these two credits quite as nicely as you might like.

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Finally consider the "unreimbursed medical expense" deduction, available for expenses that exceed 7.5% of your income. Generally, deductible medical expenses must be required by a doctor in writing, though you're probably fine getting the doctor's note now under the circumstances.

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Congratulations you're also now an employer and may have a "Zoë Baird Problem" depending on how long this has gone on. You are required to file forms 1099-ENT to report the babysitter's income. Watch out that deadline is February 1st 2021.