Well done for getting out there! My start a few years ago wasn't much fun but was well worth it now.
Maybe it's worth soaking in a nice hot bath after your run? Whenever I go out for a long one, I warm up my legs in the bath (after a good stretching session) and then maybe even rub some nice cream on them (I don't live in the UK but there must be a great sports cream you could massage into beaten legs? - someoe here will have a suggestion)
Keep it up! The start is always hard but suddenly it gets easier and you will be having fun! Keep on running into spring... that's the best time to be out if you ask me... from there on it's smooth going! Good luck!
Your post made me think of the first time I was out - new year's resolution. I was NOT going to be seen in daylight so out I went in the early hours and managed... well, maybe 10 minutes before I thought I was going to pass out! Next day I was so sore I could hardly get up the stairs...
Today I live in a very hilly area in Switzerland and I enjoy the ups and downs... I've lost a good amount of weight and running keeps me sane.
Keep at it! Download podcasts or listen to nature... run, walk, whatever... just get out there and enjoy yourself. You are doing a great thing!
I live in Switzerland and it can get nippy here... if you're talking 6-8°C then I normally go for my long (not winter thick) tights running trousers. On top I wear a thin long sleeve thermal top with neck, a running tshirt over the top of that plus a wind resistant running jacket. Hat on top. Plus a reflective band on a leg or two and a head torch (I'm out in the sticks).
You'd never get me out in shorts at those temps. I can't run like that. But I do know there are quite a few "shorts-only" people running on this forum. If you're run was crap, try dressing up more till you've found what works for you. I hate getting cold, but enjoy a warm sweat.
I have small kids and I find running a great way of getting rid of stress. Whenever I get worked up with them I know I can go for a run and get rid of any tension later. So far it has worked wonders on my mental hygene and whenever my kids realise that they are driving me nuts they'll say "don't worry, you can go for a run when we're in bed". Lovely.