I'm not aware of any chemicals that are inherent in steering wheels that can cause the things you mention. Certainly they are an incredibly dirty part of the car - often compared to a public toilet seat in terms of hygiene which is why so many cleaning produts exist for them.
If you are concerned about chemicals being added (ie doping) then take a pack of wet wipes, clean and dry the wheel before use and the problem should go away once the drugs in your system are metabolised.
If you are concerned about having been exposed to something then go to your GP, tell them your concern, detail the symptoms including the timeline of changes you experienced and if there is a risk of something remaining in your system then they can test for it.
One thing to consider before going to the GP is if you have a history of paranoia then this could make it harder to convince them. You may be better off working to prevent contact with the potentially affected surfaces by a mix of cleaning and use of gloves. See if symptoms improve and if they do then you can consider steps (eg installing a 360 degree dash cam that is motion detecting) and see if anyone is tampering with your car.
