It depends on whether the officers reasonably tried to identify the correct property. This is difficult to do from a fire escape serving two apartments, and the important thing is not whether they got it right but rather whether they tried to get it right. So long as they made some effort to identify the apartment, such as looking for numbers on the fire escape (irrespective of it they're there or not), that will do.
The linked case is not directly analogous as the police did have a warrant; they just raided the wrong house. The case was not about whether Fourth Amendment rights were violated (that was conceded), it was about whether the police had qualified immunity for the mistake (they did).
In your situation, they need probable cause (a report of a burglar? check) and exigent circumstances (a potential ongoing burglary? check); Payton v. New York, 445 U.S. 573 (1980). Unlike the linked case, there is a coherent argument that this was not a Fourth Amendment violation - a police officer could reasonably conclude that the apartment was the right one or that the burglar had moved on to your apartment since the call came in - that would give probable cause and exigent circumstances.
If it's determined that there was a violation of the Fourth Amendment in your case, the remedy would be for the government to cease the violation, which they appear to have done. While the castle doctrine protections against unreasonable search or seizure may have been violated, it's important to note that nothing the police found has been used as evidence against you, and nothing has been taken.
While the entry itself may not have been a violation, conducting a warrantless search would be unreasonable as there was no probable cause (for the search, not the entry) and exigent circumstances; Payton v. New York, 445 U.S. 573 (1980). However, if you kept something unlawful in plain view so that it could be seen from the fire escape, using that against you would not be a problem; Maryland v. Macon, 472 U.S. 463 (1985), but if they had to enter to see it, it would be inadmissible.
Police officers have a legal protection called 'qualified immunity' for anything they lawfully do in the course of their duties. This means that even if they made a mistake like entering your apartment, it may not be enough to succeed in a lawsuit against them. However, a suit based on a violation which has ceased and which caused no damage would be moot anyway.
