Hello! No, it will not ruin your cookies at all, though it will change their texture and flavor profile slightly. Brown sugar contains molasses, which adds moisture and a rich, caramel-like flavor. White sugar, on the other hand, will give your cookies a crisper edge and a lighter, sweeter taste.
If you only have white sugar, you can still make delicious cookies. They will just turn out a bit crispier and spread more during baking. As a budget cook, you do not need to run out and buy more ingredients.