Your delivery address seems to indicate otherwise: mail comes from "<blah>.members.linode.com" which appears to be a cloud hosting service. That would seem to fit the definition of reliance on a third-party service (unless you own and operate linode.com).
A problem you may run into, if your system takes off and attracts many users, is abuses which result in you being black-listed by anti-spam databases like SORBS, SpamCop and Barracuda. I suspect it will be hard to get de-listed, based on the service that you operate.
Since black-listing is by raw IP address, you might make your hosting provider upset. Suppose linode.com dynamically reshuffles a pool of IP addresses among users. You could get some IP addresses black-listed, and then those IP addresses could be cycled to another user under members.linode.com, who then has a hard time sending mail because of you.
I meant to say that I am not using any third party mail service api for sending mails. and yes you are right that I am hosting it in linode which is a cloud hosting service provider. But I have tried to put multiple filters inbuilt into this service to make sure that chances of arising above mentioned situation is low.