No, filing separately will not fix the issue. The limit for both of you is $8,550. The maximum a married couple can contribute is $8,550, even if one of you had a family plan and the other had a self-plan. See IRS rules for married people here: Publication 969.
To avoid a the 6% excise tax penalty you should contact the HSA provider to withdraw the excess $4,300 (and earnings) before the tax filing deadline.
