Go ahead and invite an electrician to give you a quote for the work you want to have done. There isn't an easy fix. A 15 amp circuit is going to be overloaded with an air conditioner in addition to a few lights and appliances.
All these internet experts and no one has said yet that there are to many items on one breaker and where I live it is illegal. It looks like someone just add more wire to the plug and ran to somewhere else. It is a recipe for a fire.
You need two things: an electrical contractor and a bank loan officer. Good luck!
you first look at the breaker box.. do you have room to add more breakers? if you can go look at the main power supply and the allotted amperage going into the home if the house draws more amps than is available you will trip main breakers.. if this stuff hasnt been updated you may need to do so and this stuff gets costly. even a small midsized 8000 BTu ac unit draws 6-8 amps and if the breaker is a 15 amp one thats half of your available load. your computer may draw 2 or 3 amps when at full load and a washer may pull 15 amps by it self and ceiling fans with a motor and four lights may pull 3 or 4 amps. you may need two or three breakers here. if you continue to over load the circuit like this that breaker may fail and burn down your house.. breakers arent there to protect the appliances they are there to protect the wiring. From the sounds of it it wasnt done even remotely correct if you HAVE to have the ac unit running unplug EVERYTHING on that circuit dont just turn off but un plug. if the ac unit is smaller like stated yeah you may be able to run the lights and PC with the unit any more you are risking damage to your home.
We bought our house late last year, has a ton of upgrades, but its an old home (1927), and the electrical was one of the few things not updated (Though there's no "problems"), One of the breakers powers 3/4 of our living room, ceiling fan, washer, and the 2 outlets in our master bedroom upstairs.
The problem were having is the breakers always tripping, and since the weathers warming up and the house doesnt have central AC (Yet), we have a portable unit upstairs, and its on the breaker that shares half the living room. However, the only things we have in the living room on those outlets are 2 lamps with low wattage CCFL bulbs, my desktop PC and monitor, and the ceiling fan is usually on low.
Is there a way to break the circuit up or something? Or can we somehow get a dedicated breaker to that AC unit? Even when we get central AC, we like our bedroom ice cold at night, so I have a feeling we'll still use the portable unit up there.
(Not looking todo this work myself, but would like to know what I need done, or if there is something I can do myself)