Welcome to the forum
Firstly, I need to mention how lucky you are to be able to walk along the beach, taking in the fresh sea air, the ability to admire the beach houses and let the sand work as a scrub on your feet.
Though I can understand that the beach is not exactly ideal in the colder months. I used to live by the beach but am now about 15mins from it, and with Sydney traffic, there's no way to make it to the beach, walk, then be at work by 8am!
Congratulations on the loss that you made previously. You may feel disappointed that you have regained some of it but at least you know that you CAN do it and you did not regain more than you lost initially - so that should be some consolation. You WILL be able to reach your goal again
As for jogging, why not try with small bursts of jogs. eg start with 30 seconds, then take it back to a walk and when you have recovered try another burst and so on.....over time you can build up the bursts of jogging and eventually you will be able to run the entire distance. It won't happen in a couple of weeks, you will need to build up to it.
Best of luck!