I'm going to go swimming正确吗?

正确,这个句子是一般将来式,还可以改为I will go swimming.
1. VERB游泳;游水 When you swim, you move through water by making movements with your arms and legs.
She learned to swim when she was really tiny... 她很小的时候就学会了游泳.
I went round to Jonathan's to see if he wanted to go swimming...我去乔纳森那里看看他是否想去游泳.
He was rescued only when an exhausted friend swam ashore...当一个精疲力尽的友人游上岸后他才获救.