Hi Laura. Can't comment on the asthma there's different kinds and it can be brought on by different stimulii for different people. Probably best to discuss your running aims and asthma with your GP.
With respect to the sore legs
- Wear full length running tights when it's cold.
- Run more frequently but shorter and slower initially. Increase distance slowly. Cardio fitness increases more quickly than bones, tendons and muscles.
- Buy an ice bag and massage your shins with it after every run for 20 mins or so.
I only started running seriously 9 months ago and went through a period where every time I stepped it up I got shin splints. I was given the above advice from an experienced triathlete friend of mine it worked for me. Feels a bit frustrating at first running more slowly and less far than you feel you can. But it worked for me.
Good luck for the Lincon 10k