First off, a 34min 5k is not bad at all. I'm glad that the tri inspired you to run more, that's great!

I think that the run/walk method might benefit you quite a bit especially since you are looking at doing the longer distance of a 10k.

When I start feeling really beat at a race or during a long run that is what I do & my pace actually levels out to being relatively the same as it would have been had I been able to get over my tiredness to run the entire time.

I know there are several women on this site that use that approach from start to finish of their race & they will have better input for you than I do. The only suggestion I have is that each person is unique in how much of a walk break they need before starting to run again so experiment.

HTH and welcome!