Trying to keep heater off-making me sick with the dusty air

I have tried to stop relying on my heating system. I think my heater is the reason I have been sick a lot lately. I noticed that when the weather is warmer and the heater is off, I feel fine. Then once I turn on the heating system, I start sneezing and coughing. The main reason for this is that I think my furnace is dirty. I have done all that I am capable of doing though. I have cleaned the furnace filter, I even replaced it with new. I also have vacuumed out the inside of the heating system. Nothing seems to fix the dusty air quality in my home. I know if I really want to tackle the issue I need to invest some money in my HVAC equipment. I either need to purchase an air purification system or call a HVAC business. I either can put the air purification system right in the furnace to clean out the dusty air or have a HVAC technician professionally clean my system. I really don’t have that money in the budget right now. So what I am currently trying to do is keep my heater off as long as I can. I keep waiting for the weather to turn warmer. Right now my hometown is experiencing temperature ranges from 40-60 degrees. So certain days requiring heating and others do not. This is horrible for my heating system and HVAC bills though. It is better for a furnace to stay on with a constant temperature rather than turning on and off rapidly. I think my energy bill this month is going to be just horrible.

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