the best scenario is that it's temporary and you won't know that until after your next run
the worst scenario is that it's plantar fasciitis (PF) which gives symptoms as you describe (heel pain 1st thing in the morning but fine when running) but it could quite easily be something else such as an achilles problem. these things can appear out of the blue even with experienced runners.
you need to isolate where the pain is - if it's under the heel on the pad at the foot rear, that my be PF; if it's above the heel it's possibly an achilles problem.
either way, see what it's like after your next run and if it's still there go seek advice from either the GP (who can be useless diagnosing running injuries if they aren't runners) or a physio with experience of running issues.
sadly if it is PF it can take some time to get over that - I suffered most of last year. catch it early and do the recommended exercises and you may be lucky and have a short episode