It’s not like there are people checking for immortals, I think it would be flagged by a dmv employee or something when they dont believe a clear 21 year old is actually 150. Let’s assume it’s current day im caught and not bring speculation on what the US is like in the year 2139 is like.
And that mistake gets more and more likely over time. An immortal would have had a much easier time 100 years ago. Even much more recently my first drivers license was paper where i was able to change my age with a pen (probably helped that it only had to fool bartenders). Now you leave a trail everywhere