First, don't be defensive of your age. I don't care. I'm not telling you something because of how old you are or how old you aren't. I'm telling you because it's going to serve you well in the future if you actually know what a ramp inspection is instead of writing on a message board "zOMG! I almost lost my career today!!!111!!1one" because the big bad ASI was hanging out at podunk county airport.
Second, I don't believe you were flying without the proper endorsements.
You need 3 signatures to be legal on solo day. One on the back of your medical/student pilot certificate and two in your logbook for your initial solo.
1.) Your student pilot certificate will carry an initial endorsement and date for the aircraft type you're allowed to solo in. If you're only using a Cessna 172 you will only have one signature here. I'm not sure I ever encountered an issue with this expiring but the only situation where it may would be a reissued student pilot certificate because the first exceed 24 calendar months.
2.) Your logbook will contain a Presolo Aeronautical Knowledge endorsement referencing 61.87(b) with an airport, aircraft type and date.
3.) Your logbook will contain a Presolo Flight Training referencing 61.87(c) with an aircraft type, limitations area and date. Limitations such as ceiling, visibility, crosswind, tower in operation or any other item the instructor feels necessary will be listed here.
With these endorsements you are free to get your shirt tails cut and fly solo 90 days hence. I would do these for my students on the same day of their first solo or at least on the day I planned to be a first solo if weather conditions didn't allow solo flight that day.
90 days after the date on those 3 endorsements you would require an endorsement for each additional 90 day period referencing 61.87(n). At no point does anywhere mention an "initial 90 day period" but rather "additional 90 day periods" for the aircraft types. Your initial solo endorsements will not contain the phrase "90 days" just as your solo endorsements themselves won't either. If it's printed in the logbook it usually has a header that says "each additional 90 day period" but the full word endorsement doesn't contain it.
I went and pulled out my first logbook to verify and that's how it was done. Initial Solo in the month of September in a Cessna 172. Additional 90 day endorsement for a Cessna 152 (as well as an endorsement on the back of my medical/student pilot certificate) in November. Additional 90 day endorsements for the 172 in December, another in April and May each with different weather conditions eventually going from an initial requirement of 10sm Visibility and <5kt crosswind component down to VFR and a 15kt X/W component. I was cancelling flights due to weather conditions and after flying with an instructor during the days I couldn't solo eventually got the extra leeway. 2 logbook endorsements (presolo knowledge, presolo flight training) and 1 endorsement on my medical. It sounds like you have these.
