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:
https://www.personalcapital.com/blog/taxes-insurance/when-does-married-filing-separately-make-sense/....
