I can definitely relate to the inability to burp. I'm 40, have been diagnosed with reflux (from which I have also had problems with heartburn), IBS, and possibly a hatial hernia. Like most previous comments, I've always had that annoying and frustrating growly-throat thing going on, and would get the hiccups often.
However, within the last few months, the most amazing thing has suddenly happened - I began burping! Completely out-of-the-blue, I can now burp without issue. I actually burp quite a bit these days - but seem to be able to, for the most part, suppress it when in public. I can't burp on command, but I won't get picky about it.
And I have to admit, it feels wonderful! My reflux has been so much more managable - as in, I haven't had to take any medicine since the ability to burp began. After 40 years of pent-up bloating and gas that I couldn't control, and those loud - and sometimes painful - throat gurgles, finally being able to burp has been incredible!
What has changed? I don't really know. The only thing that immediately comes to mind as having started about the same time is that I began going to a chiropractor for some neck and back issues. Might be coincidence, but I have nothing else to go on.