well done! the first result is always good ... it's your pb after all.
you can improve by training regularly, i'd say at least 3 times a week. balance your training sessions between longer and shorter runs. example: 5k, 8k, 12k. include a speed training once every two weeks.
above all: run outside! much better, more motivating. enter a race, you'll find yourself running much faster than in trainings.
these are just the basics, but you can find more accurate training plans online.
foodwise, i'm not an expert, but i'd say carbohydrates are fine. a good habit would be to replenish your liquid intake and eat a banana or two soon after the run/race and then fix yourself a larger meal aftwrward.