I would try a Bridge to 10k training plan so that you can structure your training. Here is an example of one but don't be afraid to run and walk to build up the distance.
Each workout includes a 5 minute warmup walk and 5 minute cooldown walk Week 1 Duration: 53 min.
Run 10 min/walk 1 min Repeat x 4. Week 2 Duration: 57 min.
Run 15 min/walk 1 min. Repeat x 3. Week 3 Duration: 63 min.
Run 17 min/walk 1 min. Repeat x 3. Week 4 Duration: 66 min.
Run 18 min/walk 1 min. Repeat x 3. Week 5 Day 1: Duration: 55 min. Run 22 min/walk 1 min. Repeat x 2.Day 2: Duration: 61 min. Run 25 min/walk 1 min. Repeat x 2.Day 3: Duration: 71 min. Run 30 min/walk 1 min. Repeat x 2. Week 6 Duration: 70 min.
Run 60 min.