It's an old rule never to
It's an old rule never to increase more than one of the following at a time: frequency, distance, speed.
Whenever I have violated this rule, I have injured myself. The problem with these injuries is that you'll have a couple of great weeks, then suddenly, bam, you have an injury. Only in retrospect do you realize that it's TMTS. BTW: I do not agree with the 10% rule. I was increasing with just 5% a week and I still ended up with a stress fracture, because I was combining with intervals.
So, be patient. Do one at a time. It's best to increase frequency first, then distance, then speed. Based on your reported distances, I recommend just working on your distance (or frequency of runs) for another 6-10 weeks, then start thinking about speed. You might want to do some easy Accelerations first (see below).
That said, there are lots of different kinds of intervals--and at least double that number in interval philosophies. Here is what I like and do:
1. "Accelerations": these are moderate, and can be combined with increasing frequency ore distance. On a normal run, you slowly increase your speed until you reach about 90% of what you could do. Then you go back to running normally for while. They only last 200 meters. You can do 3-6 of them in a workout. The object of them is technique: i.e. getting your legs and feet used to moving fast. So, concentrate on technique and don't start going faster until you think your technique is good. They are really good early in the season or when new to barefooting. You can do them also like a classic fartlek, i.e. as your mood strikes you. They should be fun, not strenuous.
2. Classic sprints: also 200 meters, but all out. These should be alternated with just short (1-2 min.) jogging pauses. After a good warm up (20 min.), do 10 in a row with pauses, then a warmdown. Then go home. If you did them right, you'll be toast. Definitely give yourself a day of recovery afterwards. Don't increase distance or frequency when doing these. Don't do them more than once a week. I would also avoid them until you have done several weeks of Accelerations, and you are confident that your technique is good.
3. Intervals: usually 1000 meters or about 4-5 min. These should be done at the maximum pace that you can sustain evenly for the whole distance. And, the last interval should be just as fast as the first (if it's not, you went too fast). I do just 3 of these in a session, sometimes with just 4 min. jogging pause in between, sometimes longer, depending on my mood. These will improve your speed for 5km to 1/2 Marathon races. Again, they should not be combined with increasing distance or frequency. Best just once a week. If you notice that your technique is slipping, then shorten the interval or slow them down. There is no sense in training to be fast with bad technique. Go back to the accelerations for a while.
I only do 2 and 3 in the 2-10 weeks before a race.
Listen to your body: if you are not in the mood to do what you have planned, then don't.
Most important, make sure it remains fun.
Best of luck,
Paleo