Could I have lead poisoning if I like to shoot at the shooting range?

Unlikely. I think it's unlikely unless you are holding lead bullets or shot in your mouth or are eating meat with lead shot still present.
Unlikely. Before OSHA rules went into effect,the most common group with adult lead poisoning were workers in battery recycling centers where lead was smelted and it entered the air/contaminated their gear. Exposure at an indoor range would be more than if outside. You could have a simple blood test done if concerned.