Yes. It is normal. As long as you are not experiencing pain above a scale of 2-3 out of 10 on your runs, or it gets progressively worse, you should be ok to slowly ease back into running as LONG as you are icing the sh*t out of you ankle and achilles and also doing some calf raises and stretching for your calf. You need to make sure that the injury site is getting adequate bloodflow after running, otherwise it's going to get worse. The WORST thing you can do is go on a run, and then sit and "rest" on a couch or chair without icing and elevating the heel/ankle. If you have to sit for long periods of time (at work) then practice range of motion exercises such as writing out ABC's with your foot or picking up objects with your toes. Even just moving your foot in all directions like flexion/extension, inversion/eversion/, abd/add will make a world of difference. Also, again, plenty of RICE! 20 on 20 off for ice.
If you are smart, you *should* be ok.