My grandparents gave me 1 acre of land, but never gave me the deed, what can I do to prove ownership

Property law is highly localized, so there may be some elements unique to Georgia. However,with that said, the general rule is a contract to convey land must be in writing. There is an exception, though. If the person receiving the land has relied upon the grant to his detriment, the person giving the land may have to honor the agreement.

Your grandparents gave you a gift. You relied on that gift and invested money to build your home.The gift is irrevocable. That is your grandfather cannot take it back. There are some problems of proof, of course, but the fact that you built your home is very much in your favor.

Have you paid taxes? There is a theory known as adverse possession that might help you. That doctrine allows you to gain title to land after possessing it for a specific period of time and meeting specific conditions. The 13 years may be enough, depending on the Georgia statute.

You definitely need a lawyer, but you have a very good chance of success.