Baron 58/58TC
Flight Crew Private; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 60; Flight Crew Total 685; Flight Crew Type 110
Time Pressure; Situational Awareness; Distraction; Confusion; Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
I received my IFR release from ZZZ Tower to ZZZ1 (clearance in part:  Alt 8;000 feet; Hdg 350; Altimeter 30.24) and was cleared for takeoff on RWY XXR.  The preceding aircraft; Aircraft Y; had taken off with announced VFR intentions to the north.  I believe Aircraft Y pilot was told to fly 350 and climb to 8;000 as well.Upon takeoff; I initiated a turn to 350 and started climbing to 8;000 feet; I turned on the  autopilot with altitude pre-select set at 8;000 feet.  ZZZ Tower asked whether I had Aircraft Y that had just taken off in sight.  I reported that I did (it was way too close in my view; and I was closing the distance much too fast in my Aircraft).  I was switched over to ZZZ2 Departure who told me that traffic was two miles at my 1 o'clock at 8;100 [feet].For reasons that I do not know; the autopilot disconnected.  I briefly looked down to adjust; decided to hand fly; and when I looked back outside; I could not see or find Aircraft Y. It wasn't a visibility issue; I just couldn't locate it.  I switched over to the TAS screen and it looked like Aircraft Y was 200 feet above me and trending left toward my flight path (trend line).  I briefly lowered the nose to improve visibility and still could locate it.  As I was climbing at about 1;250 feet FPM; and I had rising terrain (mountains) to my left; I was uncomfortable turning left and/or descending below him.  I did not want to turn right as that was the reported and indicated (TAS) direction of Aircraft Y.  I elected to get some elevation between me and Aircraft Y.ZZZ2 Approach called out my altitude; approximately 8;200 feet and asked me to correct.  I tried to respond but stepped on other traffic.  He had a brief period of being pretty busy.  He informed me of my altitude a second time and gave me the altimeter reading of 30.24 (He no doubt thought that I had not set the altimeter correctly.  I did not.)  I did climb quickly to ~8;500 feet as I was very uncomfortable when I lost sight of Aircraft Y.  The TAS did not issue an oral traffic warning as it wasn't indicated.I finally found Aircraft Y in my line of site and immediately adjusted my altitude back to 8;000 feet and initiated the turn to the east as instructed.  I should not have been cleared to take off so quickly following Aircraft Y; (a much slower airplane) on the same initial heading and altitude.  When I saw the traffic on climbout; I should have immediately told ZZZ2 Departure of the traffic upon reporting in.  The Departure Controller was busy and I should have been more forceful being heard.  I should have briefed better.  As a pilot with mostly low elevation experience; the mountainous terrain got my visual attention.  I felt boxed in with rising terrain to my left and my concerns about traffic somewhere in front of me; coming from the right. In fact; I had options to deviate lower to avoid the traffic.  But the visual out the window didn't make me feel that way.  I was heavy and with ~8;500 feet density altitude was uncomfortable with the airplane's calculated single engine OEI performance(not much ability to climb) and didn't want to sacrifice altitude.  A better answer would have been to fly lighter to reduce that performance consideration.The biggest mistake I made was not to 'barge my way in' to get the departure controller's attention that I was deviating for traffic.  I should also have asked directly for his assistance in locating it.  I was too passive because he was busy.  That isn't the right choice to make and I will do it differently in the future.
Pilot reported overtaking previous slower departure which pilot lost sight of due to cockpit issue resulting in a NMAC.