The first one is correct, huh ?

Andy and I are available : Yes. 100% correct. Perfect grammar (but ever so slightly difficult to say) Me and Andy are available: Maybe. I say this. Schoolteachers will tell you that it's wrong, but in fact it's very widely used. I think that it's acceptable in informal contexts, and it sounds natural to most people. It's also easy to say. I and Andy are available: No. This sounds horrible. It's awkward and unnatural, both to say and to hear.

If in doubt, remove the other person and see which pronoun you would use it if it was just you. I went, I am available etc . The fact that another person is involved does not change the pronoun used to refer to you. I am available; Andy and I are available (the am changes to are, but the I doesn't change).