Like caregiver222 says, carbon monoxide has no odour. You may smell other fumes that may make you feel unwell.
Carbon monoxide poisoning will not give you back problems nor make you feel "sore". I know, I actually experienced carbon monoxide poisoning. I felt very nauseas and very ill for quite a long time. When exposure to carbon monoxide happens you may also feel very tired and sleepy and prone to infections. A hospital would be able to check your blood to see if you have poisoning by this gas. But once you have been breathing in fresh air, the gas will be much less inside your body.
For carbon monoxide poisoning, you would be placed in a compression chamber. But this would need to be done straight away and not weeks afterward exposure.
Get your car checked out thoroughly by the garage and get things put right that need putting right, especially the exhaust if this is emitting fumes that are above what is the legal limit.
As you have been coughing, it is likely your body feels sore from that. The head pressure and cough may be because of sinus congestion.
Don't use your car until it is checked out.
Book an appointment to see your doctor and get your back problem looked at as well as the headaches and cough.
You can purchase quite cheaply, carbon monoxide monitors.
Talk to your doctor about your concerns.
Carbon monoxide is colorless and has no smell. There are inexpensive carbon monoxide detectors available at many stores, such as Home Depot. In the case of carbon monoxide the gas binds itself to red blood cenns and stays there for a long time. Ordinarily, it will work it's way out of the system within three weeks. There is no specific treatment except fresh air and avoid re-exposure. A broken exhaust system is the most likely way for this gas to enter the compartment of a vehicle. Have your car up on a lift and examine the connections. Clearly there should be no odor within the compartment. Back pain is generally not associated with CO toxicity. Headaches are. There should absolutely be no odor of gasoline. I'm not sure what "getting checked outy" means. CO exposure (except in severe cases) has no treatment protocol. It gets better on its own. As to the other problems, they tend to be self-limiting. If thr back problems don't go away after a month or the pain is severe professdionasl advice is probably warranted.
I do not think that this is carbon monoxide poisoning but you do need to have yourself checked out.