Can I claim for child care credit? I pay all child related expenses(including nanny) and I file married but filing separately. Both me and my husband work full time.

[MinhT1]

The IRS says in this document:

Generally, you may not take this credit if your filing status is married filing separately. However, see What’s Your Filing Status? in Publication 503, Child and Dependent Care Expenses, which describes an exception for certain taxpayers living apart from their spouse and meeting other requirements.

[Opus 17]

No.  Congress disallowed the credit for MFS, except in the case where you have been living apart from your spouse for the entire last 6 months of the tax year.  (This generally applies to a marital separation, but can sometimes also apply if your spouse is incarcerated or deployed overseas.)

It is almost always better, for this and many other reasons, to file jointly.