22-year-old lady here. I started running in eighth grade (2005) when I was about 12 or 13 years old; I ran JV cross-country for what would be my future high school. Before running cross-country, I played soccer, and I'd been active all my life, so I wasn't going from couch potato to active lifestyle just like that. Then again... playing defense for a local rec soccer league didn't really lend itself to having stamina or being fast over anything more than like... a soccer-field length. My first 5k, in 2005, was something like 28 minutes.
Before my first high-school season, I'd go to the local track and alternate between running a race-pace lap and walking a lap, then when I felt comfortable at the end of the race-pace lap, I'd make it two race-pace laps, etc... and just built up over time until I could do a 5k on the track at race pace. I had consistent injuries throughout my HS XC career, but freshman year I ran a 22-something, and by senior year I was the top female runner on the team.
By the time I got to college, I was running low-19-something 5k's and got recruited to run D1 cross-country for my university, but a year-long battle with sciatica ended that dream before it was realized; at that point, I transitioned into ultramarathons and I've been racing those ever since. The nature of training for a long, slow effort versus a fast, short one has been (knock on wood) more merciful on me, injury-wise.
So, to answer your question - yeah, it's definitely normal. You're probably going out too hard - but that's typical when you're just getting started, imho. The more experience you get as a runner (at least in my experience), the better you get at pacing yourself, gauging how long you can sustain your current intensity; when I was seriously racing 5ks I could gauge my pace fairly accurately based just on my RPE. You get to know your body pretty well the longer you train - you get more in tune with it, I've found.
You'll get there. You can do it. As my coaches would always say back when I was struggling through training runs when I first started, the most important thing is to just keep going. :)