我从儿子染上感冒了- I caught a cold from my son.
我的儿子给我一个感冒了-My son gave me a cold.
我儿子给我他的感冒了-My son gave me his cold.
1) 了 is directly placed after the verb to express past tense.
2) and 感冒 doesnt have number, its uncountable.
so the verb for someone influences someone with the cold is 给 or 传染(shortname: 染), they all work the same meaning with same grammar, just 给 is more oral speaking, 传染 is the acdemic way.
hope you like my answer.