It looks like my Sim card is has cardboard on one side am I supposed to remove that because I can’t get it to fit in the Sim card

Yes. Your iPhone 13 uses a nano-SIM card. If this is what you have, it may have been provided on a "protective" sleeve which the card would fit into.

Ref: Find out which size SIM card your iPhone or iPad uses - Apple Support

Your iPhone 13 Pro requires a Nano sized SIM card. You may have a one-size fits all SIM card. You need the smallest size SIM card. From your description, it appears that there is a corrugated (cardboard) frame around the Nano size of the SIM card. If this is the case, then remove the cardboard around the frame of the smallest available size and then it should fit the SIM card tray of your iPhone 13 pro. Be careful so that you do rip or tear the SIM card itself. The surrounding cardboard should be perforated and will come off with very little force.

Axel F.

I meant to write, Be careful so that you do NOT rip or tear the SIM card itself. The surrounding cardboard should be perforated and will come off with very little force.

Axel F.