I said "aircraft on the runway", to which I was told "you could have made it you had 1/4 mile".
Did you make clear that you were a student pilot, on an early (first?) solo? Never been to Gloucester in particular, but I know a lot of experienced controllers at towered fields with a lot of GA traffic are very good at judging the performance of their home-based GA and will sometimes sequence traffic very close behind each other.
It's tight, but if you're at 1/4 mile final while another aircraft commences the take-off roll, it may all just come together, with you landing just as the others' wheels leave the runway. But that all depends on the relative performance of the aircraft involved, runway length and so forth. And it requires some experience (or nerves of steel) on the aircraft on final - getting a landing clearance at a mere 10' above the runway.
If you have somehow come across over the radio as more experienced than you really are, the tower may have judged your abilities a bit too optimistic. As an early (first) solo student, you definitely made the right decision, and the tower should not have expected you to be comfortable so close behind a departing aircraft, particulary not in bumpy conditions.
As for the tower calling the school, there's absolutely no harm in that. It may just have been a heads-up to the school, warning them that a student in one of their aircraft has made a go-around twice and possibly sounds a bit nervous. You would not be the first student who needs some reassuring words from a familiar, friendly and calm instructor over the radio to settle some nerves.
At the end of the day, remember ATC works for you, and not the other way around.