I did one Umrah after coming from Jeddah and then stayed overnight in a hotel (which is in the clocktower area).
I did a second Umrah the next day after leaving my hotel but forgot to go to masjid Aisha. Do I need to give dam or does the second Umrah count?
بسم الله الرحمن الرحيم
In The Name Of Allah, The Most Gracious, The Most Merciful
The one who is in Makkah is required to return back to the Hil (the limit for ihram) i.e. Masjid Aisha, and put on ihram and make intention for Umrah from there. 
By performing Umrah, you have missed out this necessary step of passing the meeqat, and therefore you are liable to make one dam. 
Only Allah knows best
Written by Alimah Nasima Umm Hamza
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Al-Hidayah, Imran Nyazee Edition, Volume 1, Page 404
 Ibid, Page 501 and 502