Can a severe inflammation from getting a tattoo produce compartment syndrome?

Yes but unlikely : Really bad infection can go deep enough to invoke the fascia and muscle and this can lead to compartment. This is a limb and or life threatening condition. Seek help immediately if u suspect u could have this.

Compartment syndrome: A tattoo is a process that occurs on the skin and potentially in the fatty tissue under the skin. A compartment syndrome is in the deeper layers under the fascia. Tattoo and compartment syndrome should not be interrelated.