Firsts of all you should know that any direction you come from has it's myqaat (the place you should wear Ihram at) according this hadith.
Scholars tend to say that people who are visiting Mekka without the intention of 'Umrah or Hajj don't need to wear the Ihram, but of course it would be the best to do at least a 'Umrah once there!
Now to your inquiry as you made a mistake which is wearing Ihram in the wrong myqaat you'll need to do a kafara which the Qur'an clearly states in (2:196):
And complete the Hajj and 'umrah for Allah . But if you are prevented,
then [offer] what can be obtained with ease of sacrificial animals.
So if you were aware of this before you reached Mekka you should have gone back to your myqaat and wear the Ihram. On the other hand if you didn't have the intention for 'Umrah until you reached Masjid 'Aisha then you didn't commit any sin or mistake if you wear the Ihram there!
Now comes an other point:
if you left a myqaat and went to an other some scholars would consider it as a mistake/sin (Shafi-i and Hanbali School) as you should have worn Ihram at your myqaat or at the first myqaat you passed by. Be aware if you didn't enter the area surrounding Mekka at the frontiers of the mawaqyt this isn't really a mistake or sin fore those who say you could pass by a myqaat but wear Ihram on an other so it would be permissible (like Maliki School).
Mohammad ibn al Hassan ash-Shaybani (student of abu Hanifa) narrated in his version of al Muwatta' #382 a saying of abu Ja'afar al Baqir (May Allah be pleased with him) from a speech to people of Medina, supporting this (my own translation so read it with care):
من أحب أن يستمتع بثيابه إلى الجحفة فليفعل
who ever wants to enjoy himself with his clothes until reaching al-Juhfa' could do so
The major difference between both Opinions is that some consider the mawaqyt named by the hadith mentioned above as special for people who are citizen in countries in the direction of Medina, Shaam etc. while the others say it depends on the actual direction you are coming to Mekka from (For more details see this article in Arabic)!
According to the following fatwas for each time you missed a myqaat or went ahead without Ihram you'll need to do a sacrifice in Mekka and give it to poor people there.
I don't know what is to do if you left Mekka without doing the kafara/sacrifice->this would be an other Question and i have no fatwa about that!
But here are possible solutions (but be aware that I'm no scholar and that this may be totally wrong): if you could offer the sacrifice yourself do it, if not try to do it in an other occasion or ask/pay somebody to do it instead of you!
And Allah knows best!