This is how I see your generic strengths and weaknesses in your current situation. This is not an assessment of your potential, just pointing out where your current strengths and weaknesses are.
As a sprinter, your strength is good, power is decent, speed is okay, and your saddle time is minimal.
Being a beginner, saddle time is what is most important for anyone who is starting out. The rest of the stuff a cyclist does is to improve their cycling, but without actual ride time, you won't be a good cyclist. Wattbike doesn't count, but rollers do. To get faster, which is the weakest of your physical attributes, you will need to be able to put down power while pedalling, and on a fixed gear, you need to be able to do it fluidly. A stationary bike doesn't build the neural pathways the same way a freely moving bike does. Spend more time on your track or road bike.
Your strength game is good. No need to really focus on that too much. You would be better served with replacing one weight session a week with a real bike ride.
Saddle time will improve your power as you become better at pedalling and using that strength through your pedals, and your speed will improve because of that.
You're in a really good spot as a beginner in the sense that the major solution to your weaknesses is to just ride more. Most people need to develop skill, strength, AND the will to train when they start out. All you need to do for the next six months is ride as much as you can. You can devote less time to strength in the weight room which will also help in recovering from the riding.