Small aircraft Flight Instructor reported not seeing the other aircraft and ended up taking evasive action due to being in close proximity with said aircraft. ATC had not provided assistance in helping maintain aircraft separation.

Narrative

I was cleared to depart from CRG on Runway 32 at [Taxiway] Charlie and then make a left turn south to head to the practice area. I executed my takeoff and climbed to 2;000 ft. At some point in time; ATC cleared another aircraft to depart from Runway 23 and [Taxiway] Foxtrot and cleared him to turn left on course to the south as well. At an altitude of approximately 1;300 ft.; I noticed a target on my ADS-B directly below me so I continued my climb to 2;000 ft. as I was unable to climb higher due to a TFR above me that started at 2;500 ft. The aircraft continued to fly in the direction I was going and since I was already at cruise speed of 100 kt. IAS; I performed normal passing procedures and deviated to the right of the aircraft I was passing. The aircraft continued its climb behind me and leveled off at 2;000 ft. behind me. I still did not have a visual on the aircraft until he was right behind me at about 200 - 500 ft. As I noticed the aircraft; the other traffic noticed me as well. The aircraft complained that I was too close to him and requested my tail number. When I noticed the aircraft behind me and as close as he was; I immediately started a descent to 1;500 ft. in order to avoid any traffic conflicts. I proceeded enroute to the south and performed the rest of the flight without issues.Potential contributing factors were ATC clearance for two aircraft to depart on conflicting routes - this incident happened within the Craig Class Delta surface area and as a result; was still under the jurisdiction of Craig Tower. No traffic callouts were made by ATC and no recommended headings or altitudes were given to either aircraft to avoid traffic.A TFR over Craig that restricted the ability of an aircraft to climb away from opposing traffic. The inability of the other traffic to see me due to a high-wing configuration. Inability for myself to view the traffic due to the target being directly below and behind me. The failure of the other aircraft to take evasive action when he finally noticed me. My lack of contacting ATC and asking for clarification on the traffic and pointing out a potential conflict prior to it occurring. I was clearly the one who noticed and took action first. However; I did not report the issue to ATC and request further clarification; therefore resulting in an undesired aircraft situation.The resulting undesired situation that occurred was two aircraft within 500 ft. of horizontal separation before either pilot noticed. This resulted in my needing to descend rapidly in order to maintain necessary clearance. As a result of this incident; I will in the future; contact ATC long before a potential issue and request clarification on the traffic prior to issues in order to best ensure full awareness of all aircraft and ATC personnel involved.