How can I know if I have the DLCs ?

You mean the expansions? Maybe the login screen? I don't know if it changes too if you don't have the expansion, but mine is Shadowbringer themed.
Other than that: If you already are lvl 50 and you can do the quests to unlock Samurai and/or Red Mage, you have Stormblood. Same for lvl 60 Gunbreaker/Dancer and Shadowbringer. Heavensward is a bit trickier, but you can't have a newer expansion without having the older ones (e.g. if you buy Shadowbringer you get automatically Heavensward and Stormblood as a free bonus if you don't have them already)