First, if you are only having to share with 1 other person in a lane, that isn't busy. That is a blessing. 3 or more per lane is when it is busy.
If you do find yourself having to share, make the suggestion to take sides. That way you don't have to worry about where the other person is in relation to you. You will have half the lane to yourself and the other person will have half the lane.
If a 3rd person joins the lane, circle swim. If you keep the strip on the bottom of the pool in your vision and stay on the side of it you are suppose too, then you won't have a problem with approaching traffic. If you are worried about catching up to someone, you will feel their wake as you approach them.
If you are worried about being caught, the person closing in from behind will probably see before catching you. That person will either go around you at this point or wait to pass you at the wall.
If you get to the wall and realize a faster swimmer is closing in to the wall, let that swimmer go. You won't have to worry about you and that person trying to push off the wall at the same time.