我儿子把他的感冒传给我了。

我被我兒子傳染感冒了

I think the second and third sentences can be translated in to one: 我儿子把感冒传染给我了。 The first sentece, can be translated into: 我被儿子的感冒传染了。 通常，表达从某人那受到某重病，用“传染”，不用“给”或“得到”。

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. corrections: 我从儿子那里染上了感冒。 我的儿子给了我感冒。 我儿子给了我他的感冒。 so conclusion: 1) 了 is directly placed after the verb to express past tense. 2) and 感冒 doesnt have number, its uncountable. notes: 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.

I caught a cold from someone and someone gave me a/their cold? --我被（某人）傳染了感冒&(某人) 把感冒傳染給我了 I caught a cold from my son.-我從儿子那传染上感冒的。 My son gave me a cold.-我的儿子把感冒传染給我了。 My son gave me his cold.-我儿子把他的感冒传染給我了。