Bites don't tend to have pus in them, unless you've scratched them and they've subsequently become infected.
As others have said, these are more likely to be common or garden spots than bites.
In addition, bed bugs, although on the up, are still very rare in the UK - they tend to come in on the clothes of people who've been traveling abroad, and they're quite noticeable.
Other things which might bite are also unlikely because of positioning of the bites. There are bugs, called triatomine bugs (Kissing bugs, Assassin bugs etc.) which might bite you on the face, but they only live in South America (and are huge - you'd notice them).
It's not the right time of the year for mossies, and the wrong time and geographical area for sand flies.
You'd feel it if it were horseflies, and they don't look like gnat bites (especially if you say it looks like they had 'fangs').
Ticks would bite around your ankles when you walked through grass, and generally be attached for a while.
I might be wrong but I don't think it's the right time of the year for spider bites - they usually come out in summer I think?
So, my guess would be normal zits - sorry!