You need to decide if you are focused on reducing inflammation or reducing muscle tension. I wonder if the massage is helping or hurting. If the massage is deep tissue, it may be counter productive. If inflammation is causing the muscle tension, then you are going in circles. Joint soft tissue does not heal with inflammation present because it causes undue tension.

The massage may be like range of motion therapy at a physical therapist. If the ROM exercise makes the joint sore and inflamed, it goes against healing.

Myofacial release therapy causes the muscles to release without the deep tissue trauma. It can be very helpful. Icing after MFRT is not uncommon.

Massage is often intended to cause fluid to flow through the muscles to effect recovery from strenuous use. The heat would be to continue the fluid flow to assist in the recovery.

You should discuss these issues with your therapist(s).