i became a fast runner via hard work and probably some genetic help, and my top advice is not to hurt yourself every time because it will ultimately discourage you. your body will tell your mind to stop pain, and this can be de-motivating.
i don't know if you lift or not, but, interestingly enough, strength training and cutting your running days down to maybe 3d/wk may help. you don't really want to do too much high impact training because while cardio benefits continue to rise for the first 3 days, after that it's diminishing returns and actually an increase to injury potential. you can read up and find plenty of sources on that. strength training can help you get the base you need for running fast, too. if possible, work on fast twitch recruitment and power, but you want a decent strength base before you get into either plyos or powerlifting moves. plyos are way harder on tissue than one expect just by looking at them. agility training is to be considered, too.
starting out, just challenge yourself without causing pain. if it's week 1, OK, DOMS is to be expected. maybe into week 2 if you're pushing it. but after that, if you're still in pain, you really need to change your approach.
i've been in sports since i was 3 years old, and i've been a fast runner since early-mid grade school, when i started training sprints on my own (for personal reasons: my running form was awkward due to a hip tilt). there are plenty of ways to get fast but none of them should involve increasing your potential for injury. start with lower doses and work your way back up to the distances, intensity and time you want to achieve