You don't pay the Schedule H tax during the year unless the tax was submitted on a 941 form, then you can disregard the Schedule H.
See IRS Pub 926, page 11.
If you merely paid your own estimated tax quarterly then enter that in the "Taxes Paid" section for Estimated Tax. That will put it on the 1040 line 18d to offset your tax. That is independent from Schedule H.