Servant of Cats is correct.
I would advise against signing into your iCloud on someone else's Apple device to try and sync your iCloud photos to that device as it can cause uncontrollable cross contamination.
You can sign into icloud.com using another device's browser just to look what photos you have.
However either way, you will need a trusted device already on your apple account to get two factor authentication codes. If your only Apple device is broken and you have no trusted numbers set up you will fail to sign into anywhere with your Apple ID.
I suggest you wait til you have your replacement iPhone on your old SIM, set it up, ensure iCloud photos is turned on then wait to see what sync's to your new phone. Anything else is gone.