Competing without routines is fine. In fact, it's often preferable. Since he's got sequences that he typically dances, try dancing them youself and even stringing them together while playing music and dancing by yourself.
When I was super serious about practicing on my own, I'd go down to the studio and practice there. I'd start by doing some warm-up drills and whatever "homework" my teacher had most recently given me. When I felt like I'd achieved something, I'd move on to working on dancing. I'd do the routines from memory for a while, and also work and rework any area that was causing me problems. Since I was dancing Standard, I could look up questions regarding footwork or timing in the ISTD Standard book. In the last part of my practice session I'd put on music for each of the dances, and dance "rounds." I'd start by dancing my usual routines, and after I'd gotten through them a couple of times I'd just dance around doing whatever felt natural with the music.
If you've got notes, bring them with you in case you need to look something up. When you do your drills, use the mirror from time to time to check your posture, head position, leg lines, etc etc.
If you feel yourself getting really bored and you can't concentrate, try doing something else. Make up new exercises. Dance around to something you like, making up moves as you go. Put on music and visualise yourself competing as you dance, including imagining where your teacher is and how it feels when you are actually dancing together.
Hope this helps!