If perfumes and deodorants cause air pollution, does that mean they also heat the planet?
Maybe a little, but not much. Personal care products that have a strong odor are typically associated with volatile organic compound (VOC) emissions. VOCs are not really greenhouse gases, because they are reactive and very short-lived in the presence of sunlight. However, VOCs do have a small indirect effect on global warming because they increase tropospheric ozone production in polluted atmospheres. Tropospheric ozone is a pretty important greenhouse gas, because it has a strong radiative forcing. However, it is relatively short-lived and not a driver of anthropogenic climate change.
Air pollution is generally studied in terms of human-health. These air pollutants are often referred to as criteria (e.g. PM2.5, NOx, tropospheric ozone, carbon monoxide, sulfur dioxide) and hazardous (e.g. ammonia, metals, VOCs) air pollutants. While CAPs and HAPs do strongly influence atmospheric chemistry (which can influence greenhouse gases), air pollution usually involves chemicals that have short lifetimes (hours to days). Conversely, strong greenhouse gases (e.g. CO2, methane, HFCs) are long-lived and therefore can increase steadily over long periods of time (years). This makes GHGs strong climate forcers, because climate is on the decadal scale. Greenhouse gases are generally a distinctly separate list than CAPs and HAPs. If you think about it, it makes sense that long-lived greenhouse gases generally do not directly cause adverse health effects. If they did, we would be breathing "polluted" air our entire lives! Health-based air pollution was regulated earlier than GHGs, so any pollutant that fits both criteria (e.g. ozone) would already be regulated/controlled.