Would contributing $13,000 to a traditional IRA make a difference in us paying, as opposed to a refund?

Do you have at least $13,000 of earned income from working?

yes  also I'm receiving aretirement from a previous job

Possibly.  Almost anyone is permitted to make a full $5500 Traditional IRA contribution. The question is how much will be deductible?  

For 2015, 2016, 2017 and 2018, your total contributions to all of your traditional and Roth IRAs cannot be more than:

• $5,500 ($6,500 if you’re age 50 or older), or
• your taxable compensation for the year, if your compensation was less than this dollar limit.

Even if you can contribute the full amount to an IRA, the amount you can get a tax deduction for is impacted by whether you have a retirement plan at work. Take a look at this article to see if your full IRA contribution is tax-deductible.  How much of my Traditional IRA contribution is deductible?

• Retirement plan at work: Your deduction may be limited if you (or your spouse, if you are married) are covered by a retirement plan at work and your income exceeds certain levels.
• No retirement plan at work: Your deduction is allowed in full if you (and your spouse, if you are married) aren’t covered by a retirement plan at work.