I caught the end of when you're actually fighting the alien, and here's my advice (I played on hard before nightmare came out, so it may not be as effective on nightmare) Also, if you don't want tips just tell me to shut up and I'll leave you alone.

• The alien hunts you based on sight, sound and your proximity to the objective. Don't let yourself be visible to the Alien - if you're looking at it, it will see you. You have to get to angles where you're covered, or you can only see its feet/tail. I never used items aside from the flamethrower when the alien was around, including the motion tracker. The motion tracker makes a lot of noise, I relied on the loud footsteps to track the alien. Also, when you get closer to the objective on the map, the alien will always be close to you. That's the instances when you should use the ring around-the-rosey strategy I told you about.
  
  Don't get cornered - I avoided lockers and those small cabinets like they were the devil. They were only used in emergencies. The reason being, you have no movement to help you get away from the alien, you're just stuck in one spot and at the mercy of the Alien AI to give up and go to a new room. This leads to ten to twenty minutes of you sitting in place twiddling your thumbs.
  
  Get comfortable with the alien close to you - I know it's scary at first because the alien shows no mercy and it's an uncomfortable feeling, but you need to be able to make quick cuts into rooms or around corners in order to advance in the game. You should get close to objects, peek up and around the object with the toggle key, and stay ducked while you move from point to point. Also, when I say make quick cuts, it means make a split decision to do it. DON'T RUN. Always stay ducked if you want to live
  
  Medbay sucks - The part you're on is the hardest in the game. I thought it was stupid to make the intro with the alien around the most difficult, but this part is so hard it almost made me quit the game. Stay with it, you'll be fine and it's all down hill from here!

By the way, how much faster is Jeff (the alien) than your character is at running?

Running with the alien hunting you is always a bad idea - just don't do it. It's not a matter of the alien being faster (it is way faster, btw), it's more a matter of it hears where you're going and it won't leave the room. The result of this is tons of locker deaths.