When everyone is saying anti-inflam, what they mean is NSAID (non-steroidal anti-inflammatory drug).
NSAIDs should not be used for DOMS. Among many other things, they don't do anything for it.
Chronic tendinitis they also won't help much, they'll just dull the pain a bit. You're better off using topical agents like menthol and topical NSAIDs and adding oral paracetamol first if you need more. Oral NSAIDs come after that as paracetamol has less long term sides than NSAIDs.
There is also some evidence that NSAIDs might prevent proper repair of tendons, but it's not great. Given the lack of extra efficacy over paracetamol though, it's enough to suggest paracetamol as first line instead.