Congressman Eric Swalwell is dealing with a growing pile of legal headaches ... he's now being investigated by the Department of Homeland Security.

New complaints allege Swalwell employed a Brazilian nanny whose work authorization may have expired, according to KTLA. What's more ... the gubernatorial candidate allegedly didn't exactly follow the rulebook when it came to paying her. The au-pair, Amanda Raissa Barbosa, allegedly stayed on the job while getting paid in a way that may have sidestepped labor and immigration laws.

Now, federal agencies are taking a closer look. DHS has reportedly been looped in to investigate the claims, adding even more pressure to an already messy situation.

Remember ... Swalwell has been battling a pile of sexual misconduct allegations he's denied, while some fellow Democrats and former staffers are calling for him to step aside.

Nancy Pelosi and Adam Schiff have called for Eric to step down from the race for California governor after a former staffer spoke to CNN on the condition of anonymity and said she went to a bar with Swalwell and blacked out. She says she later remembers Swalwell on top of her while she was trying to push him off ... but he kept going anyway.

Swalwell has completely denied the accusations against him.