If you are self-employed you are required to pay self-employment tax for Social Security and Medicare---that is how you are building credits for Social Security.   

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

Please explain "we both own the business."   What is the business?   How is it set up?   Is it a sole proprietorship, an S-corps, C-corps or partnership?

Are you new to self-employment?   You are posting from online Deluxe, which cannot provide a schedule C if you need to enter business expenses.   Please provide more information.

The easiest way to pay your quarterly taxes to the IRS is at www.irs.gov/payments.

If you both own the business, then at a minimum I would expect you to be reporting business income/expenses on a 1065-multi-member LLC/Partnership tax return. But maybe you are in a community property state where you can actually split things down the middle and each report your half on a SCH C? Maybe it's set up as an S-Corp and you are both employees of that S-Corp? I don't know. I'm just guessing.