Most heirlooms only work in a limited level range in their default form and must be upgraded to work at higher levels. That costs gold, and you’ll need around 30,000 gold to outfit yourself with a fully upgraded set (counting only those that give you bonus experience). You may need to spend some time on a boosted character to acquire the gold you need to outfit another character with heirlooms, but it’s well worth the effort.
Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide