Tense with the verb forget

I reckon I have a good grasp of how to use this verb when it comes to information:
1) I have forgotten your name. (I still don't remember it)
2) I forgot your name. (I forgot and then I remembered)

However, I'm not sure how to utilize it properly when it comes to actions. I would honestly always use the past simple:
3) Oh, no! I forgot to do my homework!
4) Let me get tha.... Oh no.. I forgot my wallet!
I'm not sure, but saying I've forgotten to do my homework or I've forgotten my wallet sounds strange to me. Am I right? Thank you. P.S I know the past perfect could be used, but all of my examples are situations that are happening at the moment of speaking (I've just realized I forgot my wallet, for example)