The handicap system will do the combing of 2 9 hole rounds for you. Just post your scores as per 9 or 18 holes, if you play F9 in the morning B9 in the afternoon, post it as 18 or individually 2 rounds of 9 holes.. It won't really matter much with handicap calculations. The same goes for posting a partial round of say 12 holes if you are 8 over, post a round of 18 at 12 over...
The key is post those scores with equitable stroke.
as far as your personal best goes, IMO you can call it a personal best & no one wishes to hear that you shot XX with 2 rounds of 9 on two different days or conditions. Calling it a personal best for 9 on the other hand, not at problem.