Sleepy baby after 12 week jabs

[Eminybob]

My 12 week old had his vaccinations today and he’s pretty much slept all day since.
However, he’s also been suffering from a cold before hand (no fever so they were happy to go ahead with jabs).
When he’s been awake he’s been coughing and spluttering, he’s not fed much and what he has had he’s thrown up (more mucousy than sicky - presumably because of all the snot)
So I’m not sure if it’s the cold or the vaccinations that have made him so sleepy but I wasn’t sure if this is normal and if I should think about taking him into the doctors? Any advice welcome.
(Oh his temp is 37.9 currently so think he will be starting with a fever soon - I have given calpol but he’s been coughing it back up)

Bump anyone?
I’ve woken him up to bathe him and put him to bed, and hes out like a light again. Didn’t really want to feed much, managed to get a bit into him and some calpol and he’s not been sick. He has a cough every now and then but sleeps through it.
DS1 hardly ever got poorly as a baby (or now really) so I have no idea when I should start to really worry.

I would probably be inclined to say that as long as he has no fever I wouldn't be too worried and just keep an eye on him..
It could be the cold too and he's feeling a bit groggy and just wants to sleep it off

Thank you. I should have said he was up a lot of last night with the cold so is probably catching up from that too (which is what I am going to try and do now too!)

My ds slept a lot after his first jabs, I think it was a combination of the jabs themselves, the drama of it all (for a tiny baby the whole thing seems terribly dramatic, I think) and just feeling a bit sorry for himself afterwards. He was fine within 24 hours. But it's like anything, you know your child best, if you're worried or he has a fever, stops drinking or making wet nappies etc, get him checked out. No doctor will look down on a concerned mum with an 8 week old baby.