Yes, we are in an ice age, seeing as there are frozen poles. But we are changing that, soon there will be no frozen pole caps and with that, the ice age will have ended. We are creating our own hot period.
Btw. it can only be an interglacial period if the glaciers return after. It's a descriptive term, not a prescriptive, and there is no reason why the current warm period should be seen as interglacial.
Because climate doesn't just change without a cause, it needs a driving force. Earlier hot periods were caused by volcanic CO2 and the change happened slowly, over millions of years. Earlier cold periods had a number of different reasons, from nuclear winters after asteroid impact, ultra-high plant growth with not enough O2 consumers or global darkening due to the ash of a supervolcano or even the changing tilt of earths axis.
There is no natural reason for the current warm period to turn into continental glaciation, let alone end so early and so fast, let alone the entire ice age, that has created temperatures that humans are comfortable with, just melting away around us.
We have likely ended the ice age entirely, as much heat as we trapped in the atmosphere.
Climate changes more rapidly right now than it ever did before bar the impact of ecocidal asteroids and the consequences are dire. We are heating up the planet and there is no force cooling it. If we want to stay even a little bit comfortable, we should drastically reduce the amount of energy trapped in our atmosphere.