I've lived in my home 2 months shy of 2 years and I'm wondering if I sell it now would I have to pay capital gains tax since it's not been a complete 2 years?

Unless your home was your primary home for at least 2 of the last 5 years (not necessarily 24 consecutive months), you'll be required to pay capital gains tax on the gains.  See Publication 523, specifically the "Eligibility Test".  There are some exceptions, but you'll need to review the rules yourself to see if any of them apply.

https://www.irs.gov/pub/irs-pdf/p523.pdf

And to clarify, that's 2 years out of the 5 years leading up to the date of sale (the closing date).  So just make sure your closing date (which is usually negotiable) is beyond the 2-year period.