Questions about having private insurance (through my parent’s employer) and Medicaid at the same time

I am 25 and still under my dad’s Anthem health insurance plan (it’s a PPO) through his work. I am unemployed due to disability (I became disabled at age 20) and just got approved this week to receive SSI. Since I receive SSI, I have been automatically enrolled in Medicaid (I didn’t know I would be getting Medicaid until they sent me a services card in the mail and I called to find out what it was). Am I allowed to have both Medicaid and private insurance? Will I get booted off my private insurance? I talked to a rep for Medicaid and she said that Medicaid will become my secondary insurance. Should I call anthem to find out what changes on their end now? I would hate to lose my anthem insurance because I use it to see a lot of specialists. What questions should I ask anthem? Are there any questions I should avoid asking? My parents always tell me to “be careful of what you tell the insurance company” and I have no idea what that means. Any information you have about either Anthem or Medicaid would be much appreciated because I’m still learning how it all works. Thank you for the help!

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