Negative progress

I'm a complete and utter beginner at this running lark, 32 years old
and never felt the need to go faster than walking pace before (but I've
done a little cycling). Anyhow, as I posted in the latest weekly log
post I've been getting out there pushing my very modest limits for the
past 10 days or so, and in the last week have run 4k every other day
(mostly managing to round with only 1 walking break or so). As any new
convert tends to be, I'm pretty enthusiastic about it all at the
moment.

Anyway, thing is, today I set off expecting great things and certainly
felt more comfortable with my level of aerobic fitness as I found I
wasn't as out of puff at the 1k mark as I had been just a week before.
Then it all seemed to unravel.

As I carried on I felt like my lower legs were stiffening up. Not just
that but the muscles at the front around my shins were quite painful.
Each time my foot landed there was a spike of pain. It just worsened
to the point where I was walking at 2k, not through being out of puff
(the only reason I've had to break into a walk before) but because I
was so uncomfortable. I felt like pressing on further might do damage,
so I took the sensible option of walking the rest of the way.

My colleagues at the office quickly diagnosed shin splints, but I don't
know if that's the case (I don't trust their expertise!). Now, some 7
hours later, if I press on and around my shins it feels tender, like
mild bruising, but is that what shin splints are? I'm assuming I need
to back off and take more rest days between training, at least in these
early stages when my legs aren't used to this kind of activity. Does
that sound ok or should I leave a clear week or something? Don't want
to waste too much time, but my 10k isn't till May so I guess I don't
have to get too stressed.

Advice from those who've been there and done that before would be
appreciated.

.