There are two separate terms here that look the same but are not.
There is the phrase to be after [somebody/thing] which is a combination of the verb to be and the preposition after. It has the meaning to try to reach [somebody/thing] or to pursue [somebody/thing]. Example: "She was after him to divulge the recipe for his famous cookies" or "They were after the Stanley Cup."
Then there is the preposition after simply meaning behind or later than. This can describe relativity (in time or space) in conjunction with any verb, including to be, but does not imply pursuit. Examples: "He left after her" or "She shut the door after him" or "They were in line after the man in the purple shoes."1
Your example "She teetered after him in her high-heeled shoes" could be either one depending on the context. Saying that she "teetered" means she walked unsteadily, but one can walk unsteadily behind someone without attempting to catch up to them just as one can walk unsteadily behind someone while attempting to catch up to them.
1This sentence actually sounds a little awkward to a native ear; a more natural sentence might be "They got in line after the man in the purple shoes" or "They were in line behind the man in the purple shoes" depending on if the emphasis is on when they entered the line or their position in the line. But the original example is not incorrect.