I don't know what the relative ranks of Tina Lawton and Simon Tarses might have been about a century apart and centuries in our future.
No-one does canonically, but certain posters (mostly Americans I assume), insist that Tarses - who seems to do at least some of the job of an Independent Duty Corpsman (minimum E5 promotable) or civilian pharmacy assistant (which is typically a two-year training course by itself, and ) - must be junior in rank to Tina Lawton, who is identified as "of your age" relative to 17-year old Charlie Evans just because "Crewman 1st Class" outranks "Petty Officer Third Class" in the US naval ratings. I reject that premise and prefer to look for other options.
Now I think about it, the various titles of Miles O'Brien indicate that Chief Specialist (Lawton and Rand would report to a Chief Yeoman) can be used generically instead of (Chief) Petty Officer, and logically that follows that PO1 to PO3 could therefore be expressed as Specialist 1st to Specialist 3rd, so as common sense tells us that Tarses must be a Specialist (ie rated), then logically he would be a Specialist 1st (BTW, Rand likely is as well) and Lawton would be a more junior Specialist 3rd.
Why can't someone be a grade lower in rank than someone younger in age?
So I see no reason to believe that in Starfleet every single person who has a specific pay grade must be older than every person who holds the next lower pay grade and younger than every person who holds the next higher pay grade - and even if Starfleet members don't get paid in the TNG era they do get paid in the TOS era.
I suppose it's not impossible, but as not above I reject the principle that a crewman who demonstrates considerable training and implied professional experience must be a junior crewman who has neither merely on the basis of rank equivalences during to two different time periods.
And apparently it is within Picard's authority to appoint a 15-year-old civilian an acting ensign. And Wesley is put in charge of a team investigating unstable planets as early as the age of 16 in "Pen Pals".
Yup.
I agree therefore that it's tricky to determine how experienced that Lawton might be as we are told nothing about her duties (other than that she seems to junior enough to be mainly "others started", so I typically lean towards determining relative rank based on Tarses scope of practice which appears to be mostly "self starting".