Getting DOMS when you start working out is normal and after some weeks you probably won't get it anymore, unless you add a sudden increase in workload (beyond your normal progression) or do some exercise you didn't previously do and to which your body hasn't adapted.
I've also frequently noticed that it tends to be the worst the second day after working out, and doing a workout while still having it can in fact decrease it. But that might be because a beginner adapts very quickly to any new stimulus.
That said, given how it's worse now than before, I believe you are letting the stress you impose on your body exceed its capacity for recovery. So you have two options (or combination thereof):
- Leave a longer rest period between your workouts to allow for recovery.
- Decrease the intensity of your workout to lower the amount of stress imposed.
I'd say the second option is the better one. As JohnP noted in his comment, running 45 minutes as a beginner is quite a lot. Even if you can do it during the workout, it doesn't mean the stress you imposed on your body isn't in excess of what it is accustomed to. So now you have to rest longer to recover, limiting the number of workouts in a week and reducing the efficiency.
The jump from 30 minutes to 45 is also a factor in this. The stress increase must be a bit more gradual. Going from 30 minutes to 35 would have been more realistic. You could also have increased the speed while keeping the time the same (again, in a sensible amount).
I suggest you rest now until the DOMS has disappeared, then do a 30-minute run again and increase the workload at every workout (time or intensity) in a much less dramatic way, while respecting one rest day between workouts, to allow your body's adaptation to exceed the demands placed on it.