A herniated disc is what we used to call a 'slipped disc' years ago. Technically speaking, discs can't 'slip' out of place as such. What's happened is that the disc has developed a bulge which usually impringes on the sciatic nerve with the consequential 'referred pain,' as they call it. This is pain that manifests itself down the back of the leg but actually originates at the sight of the nerve impringement. Usually with rest, physiotherapy and moderate mobility the pain subsides. Core abdominal strength is part of the key to preventing reoccurrence, but you should stop running altogether with any symptoms before you embark on any rehabilitation program. You must talk to a qualified physio about this, I can only tell you of my own personal experience. A word of caution from someone who's been there: if you develop any numbness or loss of muscle function seek medical advice straight away as in the worst case scenario the disc can prolapse , which means that it ruptures and the soft core bulges out damaging the sciatic nerve. This happened to me in 1990 and I ended up in surgery. The good news is that the surgery is usually very successful and fortunately I am still running today but it takes quite a long recovery. You have my sympathies, I know how hard and frustrating it is, but be smart and patient, I bless every day that I'm out there running the roads and fields all these years later.
Sounds like it could be a touch of peroneal tendonitis, fairly common in new runners and usually associated with 'too much too soon,' but best to get a professional diagnosis. Also sometimes associated with the 'wrong shoe for the runner,' and as rwd suggests talk to the experts in footwear. Personally, I go to 'Up and Running' where they can analyse your gait on a treadmill. Often the pain subsides when the runner backs off from the mileage/speed and progresses in a more sensible manner. With 3 months to go until May, you should have time to sort this one out...with a little patience and advice.
I had this over 20 years ago and ended up in surgery after the disc prolapsed. A prolapsed disc, if it develops into that, is unlikely to mend itself. The good news is that the surgery is usually successful as it was with mine, although I had to stop running for a long time, usually takes about a year after surgery, but that's one to discuss with the consultant. If you start feeling any numbness or loss of muscle function (as happened to me) you need to see a doctor straight away. Stop running for now, seek advice.
Scholl orthaheals are the best thing since sliced bread in my opinion. Like you I wear a pair in my workboots and have a pair for running. I'm assuming you have removed the existing insoles from yout Asics? Some shoes (the cheaper ones) don't have removable insoles. For the orthotic to be effective you must replace the insole with the orthaheal. I've use mine in Brooks, Mizuno and Asics shoes and find them an improvement in each. They work best in a neutral rather than a 'motion control' shoe. Talk to the guys at Up and Running shops to work out which is best. Also, check out 'stair stretching' but be gentle and don't overdo it. Both things worked for me.
Stretching is beneficial. The older you get the more you find that you HAVE to stretch. If you get cramp you HAVE to stretch. Stretching after exercise helps prevents this. Stuyr is right about cold muscle stretching, the muscle will resist when attempted to stretch without adequate blood flow. The runners with the greatest injury records are those that don't stretch at all and those who pre-run stretch. Hold a stretch too long and the same will happen, the muscle will resist. Current thinking is leaning towards a thing called 'active isolated stretches,' where the muscle is repeatedly held in stretch for 2 - 3 seconds and then repeated several times. This system has worked well for me for some time now, most folk my age (63) can barely touch their shins, never mind their toes.