There are a couple of things your can do:
1) lift before you run, which warms up your legs. Be sure to stretch before running.
2) lift after you run. You want to make sure your legs are warmed up, but also stretch properly.
From what I gathered, you used the leg
curl machine. This machine works your hamstrings. If the back of you legs felt tight, then you may have lifted too heavy. I would start out at a low weight, but higher reps. You want to build your hamstrings. There is nothing worse than pulling your hamstring. Trust me...I used to be a huge runner, it's painful and messes up your workout plan.
As far as running the next day, yes you can. Depending on how heavy you lift, you should be able to run. Grant it, you may be somewhat sore in the morning, but make sure you stretch your legs. Also, running can also make your legs hurt, depending on the incline, speed, and duration of your run. If you become tired and your formation slacks, your body is going to pay for it--especially in the legs.
Good Luck