Super King Air 200 pilot reported experiencing a loss of pressurization during their climb; resulting in the pilot losing orientation and directional control and flying towards terrain. The pilot regained orientation and control of the aircraft and proceeded to their destination.

Narrative

I was cleared for the ZZZZZ departure out of ZZZ; RWY XX. After lift off I began the left turn to 7100 Direct ZZZZZ1. After reaching the fix; I began the turn to follow the depicted route on the published departure. At this point the aircraft lost pressurization temporarily and both bleed air lights came on. I was hand flying the route and as I trouble shot the bleeds I lost orientation and directional control. Conditions were clear--no clouds and unlimited visibility. The bleeds came back on quite quickly. I refocused on navigation and noticed I was off course and immediately engaged the Autopilot to fly to the next fix. The day being severe clear weather caused complacency. I should have planned on engaging the autopilot sooner to fly this SID that I had never flown before. I should have planned to put the autopilot on regardless of the clear conditions just for this reason that if something happens that requires immediate attention the aircraft will still remain on the imputed course. This was my first time into and out of ZZZ. I also should have navigated prior to worrying about the pressurization since I was only climbing to 15;000 and could have easily canceled and gone VFR and then worked on the pressurization. Departure notified of a low altitude alert and were very helpful as I regained proper heading and climbed to the proper altitude. Aviate; Navigate; Communicate.