Today, January 17th, may or may not be Alex's 17th birthday. I'm far from 100% sure of this – it might have been last Saturday, or another Saturday.
I'm almost certain it's a Saturday – last year they (tried to) celebrate her birthday on the night before the school open house, Jay's football team's big game, and Alex's therapy session. Since there was no school for the kids on that following day, that narrows the night before down to Friday or Saturday. And since it's highly unlikely that a therapist (or almost any doctor, for that matter) would schedule appointments for a Sunday that would put Alex in therapy (and her parents in open house) on Saturday, meaning the birthday celebration occurred on Friday night.
Now I suppose the celebration could have been planned for a day other than her actual birthday (e.g her birthday was Wednesday), but in that case I would think it would be more likely they'd plan a party for sometime Saturday or Sunday rather than Friday night. And the fact it was an “important” birthday (her Sweet 16) probably would call for a family party on the day itself, even if in midweek.
So I'm pretty sure last year her birthday fell on Friday, which means this year it falls on Saturday. But which one?
If we assume the date the events of “Under Pressure” occurred in close to real time (remember the airdate was Wednesday, January 15), then that would make the date of the birthday party most likely either the 10th or the 17th. The case for the 17th is simple – they often air episodes (especially holiday episodes) before the actual day – this year's Halloween episode aired on October 29th.
As for an argument for the 10th, while “Under Pressure” was the 12th episode to air last season, it was actually the 11th episode produced (the production code for it is “5arg11”). That means this episode may have originally meant to air on January 8th, which could place the start of the timeline at January 10.
(Another theory I thought of doesn't hold as much water – Jay had an important football game to watch on Saturday and in real life there were no Saturday games scheduled on the day after the 17th, but there were 2 pro games played on Saturday the 11th. But that could be easily be explained away by saying in the fictional world they did have a Saturday game on the 18th.)
Now it's possible (especially how skewed some of this show's timelines are – they've aired the Christmas episodes as far ahead as 2 weeks before the holiday) it could be another date, but 1/10 and 1/17 are the most likely.
So, if it is today, Happy Birthday, Alex!