we get a -ton- of spam here, so the major free webmails are blocked. let me know your email address and i'll manually update your account
as for getting your own, it's easy, just register a domain and use the registras options to forward all mail to a gmail/yahoo/whatever address. That way you have an email address for life. if yahoo ever stop providing email, you can repoint your domain to somewhere else, and you don't need to tell anyone your new address.
I've had my spiny.org domain for about 20 years now I think, been through loads of email providers, but never had to change my email address