Not always. They sell ibuprofen in a tube so you can rub it on muscles. If you are in the US, you probably don't see it on your pharmacy shelves, though. The pharmacy I worked at didn't sell it (and it was a large chain), but all of the pharmacies I've seen in Norway have it.
In the US topical diclofenac is common and sells well - brand name Voltaren. They (topical NSAIDs) are first line therapy for acute musculoskeletal pain.
Broken_Hippo already responded about NSAIDs not always being oral.
> CBD does seem to have an effect on inflammation.
Yes but it doesn't penetrate the skin very well. That's why I sort of hinted at large dose transdermals as being a possibility, but the small bit of research that has been done is both early and mixed. I think the transdermal is a pretty critical part here and I don't know of any approved transdermal CBD products, just lotions that are useless.
