No. The two events are not related.
There are some quirks in the tax system, that you may have heard of, but they don't apply to your situation.
The old rule about selling a house and using the proceeds to buy a new house to avoid capital gains was eliminated many years ago. Even then it would not have applied to paying off a mortgage.
"Like kind exchange" doesn't apply either.
There is a capital gain exclusion for selling your principal residence. But you don't qualify because the house sold was not your principal residence for 2 of the 5 years before it was sold.
