Robert, I did some research based on the information provided and believe I can help.
The P-39 was not that widely used within the AAC so I searched on the aircraft, the date you provided, 13 AAF and Guadalcanal.
With that search, I found Navy Department Communiqué from the South Pacific. Here are the results;
N. D. COMMUNIQUÉ NO. 415, JUNE 17, 1943 South Pacific.
1. A brief report received from the South Pacific reveals that in an air battle over Guadalcanal Island on June 16, U. S. planes shot down thirty two Japanese bombers and forty five Zero fighters. Six U. S. planes are missing. 2. No further details have been received.
N. D. COMMUNIQUÉ NO. 416, JUNE 18, 1943 South Pacific (all dates are east longitude).
1. On June 16, during the night, Army Liberator (Consolidated B-24) heavy bombers attacked Japanese positions on Ballale Island, Shortland Island Area. Results were not observed. One U. S. bomber is missing. 2. Further details of the air battle over Guadalcanal Island (previously mentioned in Navy Department Communiqué No. 415) reveal that the Japanese air forces engaged were estimated to have been sixty bombers and sixty fighters. One U. S. merchant ship and one landing barge were damaged. U. S. personnel casualties were: Twenty five killed, twenty nine injured, and twenty-two missing afloat and ashore. The latest report confirms that six U. S. planes were lost, but the pilot of one plane was rescued.
3. On June 16, three additional Japanese soldiers were captured in the Khlebnikof Area, Attu Island. The total number of enemy captured is 24.
N. D. COMMUNIQUÉ NO. 418, JUNE 19, 1943 South Pacific (all dates are east longitude).
1. On June 16, a twin engine Japanese reconnaissance bomber was shot down southeast of San Cristobal Island.
2. On June 17:
(a) During the afternoon, Dauntless (Douglass SBD) dive bombers escorted by Wildcat (Grumman F4F) fighters attacked Japanese positions at Rekata Bay, Santa Isabel Island. Hits were scored on enemy antiaircraft positions. (b) During the night an unknown number of Japanese planes approached Guadalcanal Island, and dropped several bombs harmlessly into the water off Tulagi. No damage or casualties were sustained.
3. Additional reports received indicate that in the air battle over Guadalcanal Island (previously reported in Navy Department Communiqués 415 and 416) 94 Japanese planes were destroyed instead of 77. Of the additional 17, 16 were shot down by ships in the harbor and one by shore?based antiaircraft. The Japanese planes were met by Army and Navy fighter planes, participating in approximately equal numbers. The Navy planes were manned by Navy and Marine Corps pilots. Eight of the Army planes were flown by New Zealand pilots. All U. S. planes were based on Henderson Field. Fighting plane types including Corsairs (Vought F4U), Wildcats (Grumman F4F), Lightnings (Lockheed P-38), Airacobras (Bell P-39), and Warhawks (Curtiss P-40). This air victory was a striking example of coordinated battle action by the various units concerned. The Japanese planes came in over Beaufort Bay (West coast of Guadalcanal Island) and were engaged by the U. S. planes. At about the same time, another group of Japanese planes approached from farther north and were immediately attacked. Approximately 30 enemy dive bombers maneuvered to attack U. S. cargo vessels escorted by destroyers. Subsequent contacts were made over Koli Point, Savo Island, Cape Esperance and Tulagi. The dive bombing of U. S. surface units occurred at about 2:15 p. m. In this attack a cargo vessel and a landing craft were damaged. One other cargo vessel sustained minor damage. In the air action, 30 Navy and Marine Corps planes shot down sixteen Zero fighters and seventeen bombers. Thirty?six Army planes shot down twenty-nine Zeros and ten bombers. The eight New Zealand pilots shot down five bombers. Of the six U. S. planes shot down, two of the pilots were rescued.
This Communiqué shows "Henderson Field" as the station for the US AAF aircraft. Further search shows only one unit flying the P-39 Aircobra under the 13 AAF. The 347th Fighter Group, Headquartered out of New Caledonia and the 67th Fighter Squadron assigned to Henderson Field.
The 67th Pursuit Squadron was activated at Selfridge Field, Michigan, 15 Jan 41. After completing preliminary training in Baton Rouge, LA, the squadron's people and aircraft were shipped to Camp Darly, Australia, on 23 Jan 42. On 15 May 42, the 67th Pursuit Squadron was redesignated the 67th Fighter Squadron. Using P-39 AiraCobra, P-400 (a model of the P-39 and P-38 Lightning aircraft. The squadron acquired battle honors including the Presidential Unit Citation and campaign streamers. They also received the Distinguished Unit Citation and Philippine Presidential Unit Citation.