Your problem is obviously your pacing. Do you talk to your partner when training together? One trick you could try is talking out loud / singing whilst you are running. If you cannot talk then as a beginner you are running too fast so slow down, get your breath back and the try again.
If you run with a stopwatch when you run with your partner make a mental note of times you get to the end of a road / key points then when you run on your own try and match these times, difficult but it helps.