Mitsubishi Repair Problems? Ask a Mechanic for Answers ASAP
There are three different methods you can use to disarm the alarm on these if your horn is honking repeatedly (not one solid tone).
Of course first the fob which is not an option for you. The second is to use the key in the door lock cylinder (not the ignition cylinder) turned twice to unlock while the horn is sounding. If the alarm has already timed out from going off its full duration, you will need to set the alarm off again before using the key in the door to unlock twice.
If this does not work... for example the switch on the lock cylinder is faulty etc... your last option is to disconnect the negative battery cable, insert the key into the ignition and turn it to On, then reconnect the negative battery cable. This will trick the system into the disarmed state.
IF the horn is sounding one long tone (not repeated honking), then this is a sign the horn pad in the air bag has shorted, an extremely common problem. I know you mentioned the alarm and so it is probably honking on/off in which case the previous comments apply... these horn pads are super common to fail on this model though and people sometimes confuse it for the alarm going off so I always like to clarify between the solid tone and on/off alarm honking just to clear any possible confusion.