I spent the day cleaning our basement. I found mold on the concrete and cleaned it with a lot of bleach. Now I have a deep cough, is it from the mold?

Mold and bleach. It's possible that it is from both... When cleaning, mold spores and some dust flew up into the air and the bleach may have splashed a bit. It's best to wear a simple mouth mask when cleaning to minimize inhaling these particles. But be sure to take breaks from the air environment by going upstairs or outside to balance out and prevent such cough or allergic / inflammatory rxns.
Possibly... Your symptoms may be due to mold but your symptoms may also be due to inhalation of the cleaning chemicals. You should use cleaning chemicals in a well-ventilated area only. If your symptoms worsen or you become short of breath, go to the er for evaluation and treatment.
Possibly. It could be the mold, or perhaps you're reacting to the bleach you cleaned it with. It's also possibly you were going to get sick anyway and it's just coincidental get adequate rest, fluids (supportive care) and see your doctor if your symptoms worsen, new concerning symptoms (like high fever) develops, etc.
More likely bleach. The fumes from bleach are very powerful and will irritate the airways right away. Full-strength bleach is very harsh and should usually be diluted, & use good ventilation and protective gear. Most mold can be cleaned with plain soap and water; if not, call a professional.Never mix bleach with other cleaning products. Get lots of fresh air, drink water & rest, and if not better in 3-5 days, see dr.