Driver's License Issues: License Suspended --> Expired --> Moved to a New State --> Got a New License

My question involves a driver's license issued by the State of: Indiana

I was in a reckless charge in June(was driving a rental car from payless). My license wasn't suspended then. Then they asked for a document from the rental car agency or I'd face a suspension Oct-Dec. i couldn't provide the document bc Payless Rentals is trash. Meanwhile I moved to Texas, went to get my license renewed but was told that I'd have to go for a new license and I did. I just got my new licence from the state of Texas and my Indiana BMV record shows license suspended for 3months.

Now my questions:
1. Can I drive on my new license? What if I get pulled over for some reason and get charged for driving on a suspended license?
2. Can I drive with this new license in the state of Indiana? cz I keep going back to Indiana every now and then cz family lives there. So if in Indiana I get pulled over, will they be able to link it to my previous license and charge me for driving despite suspension?

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Thank you

Driver's License Issues: License Suspended --> Expired --> Moved to a New State --> Got a New License