Just because you have only one avenue of egress from your apartment doesn't entitle you to financial compensation under any law in any jurisdiction. The only recourse in that event would be to see if there are fire codes or building codes in your city that require fire escapes or secondary exits, report the landlord to that enforcement agency, and then complain to them if the landlord doesn't comply. However, the landlord could have a grandfather clause on the building whereby he/she isn't required to install fire escapes or provide alternate routes of exit.
Also, since you have been paying rent for ten months, the fact that you've paid it is an unspoken agreement stating that you accept the property as-is. If you have a written lease or rental agreement, there is likely a clause in it somewhere that provides you with no recourse, as well.