There are different rules in regards to down payments and gifted down payments. Relatives can help you with your down payment but depending on the type of mortgage you are using, they can contribute at different levels. On FHA mortgages (3.5% Down Payment required), relatives can gift you the entire amount or any amount above or below the required amount. On Conventional mortgages (5% required) they can only gift you a 20% down payment or any amount above and beyond your 5% down payment (must be your money).
USDA & VA financing does not require a down payment at all.
With 10% down and good credit you should be able to buy a home as long as the mortgage payment fits your total budget. We would love to help you if you would like a FREE pre-approval. You can apply at www.the2mortgageguys.com