Hi I want to upgrade my air conditioner from an 8,000 BTU 7.5 amp to 10,00 BTU. But
My problem is I live in an apartment with fuses the air conditioning line is on a 15 amp fuse. If the a/c is 10,000 BTU and the amps are 9 or 10 will that continually blow out my 15 amp fuse.

Depends:

A) On what else is on that circuit.
B) The fuse should be replaced with a time delay version

Code suggests that the Fuse should be the next one (15 or 20) when multiplying the Current by (1/0.8) for loads EXPECTED to be on for more than 3 hours at a time.

So, if nothing else is on that circuit, 12 Amps is the max the AC can draw.

Amps = Watts/(120 Volts); so you can estimate the current drawn by other devices on the 120 V circuit.