Married Filing separately with no dependents means your standard deduction is the smallest tier at $12,550.
Married filing jointly would get you a $25,100 standard deduction.
Filing head of household would be $18,800.
It's hard to say why you owe money without knowing what you made. There could be capital gains in there or something that is pushing it up or possibly your employer didn't withhold social security / Medicare properly.
Here is an article that might help figure it out:
Did you account for your husband's income and taxes withheld from his wages? Every dollar that you earn is added to the top of his income and puts you in a much higher tax bracket.
It is not an exact science to get as close to zero as possible, which is the current IRS plan. Sometimes you get a little back , sometimes you owe. PUB 15-T gives you the withholding tables your employer has to use, based on income, how often you are paid and your filing status.