I did my first run of week three yesterday and I'm fairly confident I've got shin splints now 
when is the soonest I should do my next run? It hurts to walk currently (luckily I've got a desk job so I'm resting them for the time being before the walk home.
Does anyone have any additional advice to maybe help with the pain? Can I foam roll my shins? or will this make it worse?
Thanks in advance for any help 
Shin pain is very common at this stage of the programme. Yes, foam rolling will help it.
And by the sound of it make sure you have the right running shoes. With good cushioning.
I bought some nice pink Nike running shoes :') was hoping they'd be okay, it's probably my form that is the trouble rather than the shoe, I'd be a bad workman blaming his tools I think haha
Even a good workman needs the right tools for the job and sometimes tools fitted just to them. I had shin splints early in the programme, what helped me was gait analysis at a proper running shop where someone who knows what they're looking at films you on a treadmill and recommends a range of shoes that are right for you... you never know, some may even be pink 
There's an exercise you can do literally anywhere, even sitting down, that will help to build up the shins. I can't remember it's name though, but it's kind of the opposite of a calf raise. It quite simply involves placing both feet flat on the floor, then keeping the heels on the floor, lift the forefoot as high as possible, hold for a few seconds, then back down again.
It doesn't sound like much. But then when you consider how little the shins do in the modern lifestyle, it doesn't take much to build them up a bit. It's basically a slow motion low impact version of exactly what happens when you run. After pushing off, where your foot is pointing down, you have to kind if lift it ready for landing. That happens so instinctively I doubt many even think about it, but that's the action that's basically fatiguing the shins. In most cases at least.
that's super - thank you!
I'd also recommend the exercise suggested by Mr Decrepit, since it'll help to strengthen your anterior tibialis (the thin sheet of muscle covering the shin), alongside the extensor muscles located closer to the front of the ankle.
However, don't neglect your calves or feet either, since strengthening them both will help to ensure that they're also less susceptible to injury and fatigue. Calf raises and towel scrunches (for your plantar) should suffice to begin with.
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