My concern is that the swelling is described by the original poster as "it all seems to hurt to the touch". That is 100% *not* just yer basic harmless windpuff, which would NOT be painful.
Honestly I tend to discount anything anyone says about "the horse is not lame", unless i happen to know...
A very realistic possibility is damage to the suspensory or deep flexor. This does not always cause hugely-obvious lameness.
Another possibility is a jar to the joint (bruising the joint capsule), or a sprain.
If there is heat in the hoof, it is even not-impossible it could be from a hoof...