I have applied at a company for an internship this summer. They replied enthusiastically 2-3 days later asking for more details. I sent them a brief description of my projects, my CV and my interest in the company. It has been a month and still no reply back. Despite this, the person who replied my email the first time turned out to be a friend's teacher in my home country. I told him to ask about internship possibilities in a subtle way and from what he told me they were interested in me and this confused me because I didn't get any reply.
I could get his number from my friend and call him to ask in a more personal way but I feel this lacks lots of professionalism. Would something among the lines of "Hello! Do you happen to have any news regarding this summer's internship? Best regards, x" be ok?
I want to leave a good impression but I'm not sure what would be suitable without seeming desperate nor cocky.