Student pilot on a training flight reported they failed to follow the departure procedure and received a Terrain Alert during their initial climb..

Narrative

On Day 0 at approximately XA:05; acting as PIC; [I] departed Runway 22R from Felts Field (SFF) and deviated from instructed departure procedure. I am in the process of working through my online ground school and today was my first scheduled flight to begin working my IFR training. My instructor and I decided to operate locally between SFF and ZZZ with departure; holding; and approaches.In the last 90 days I have been diligently working on being comfortable flying my aircraft in VMC and was excited to begin working on exploring its IFR capabilities. In today's flight wind was 210 @ 15 gusting 25. While speaking with Ground at SFF; we requested local IFR clearance for the practiced approach for Runway X at ZZZ with a hold at ZZZZZ. We were assigned departure procedure for Felts Four; and to climb to 6;000. This route does require a climbing left turn to heading 190; and then we would be assigned vectors from there. While in the runup area; myself and my instructor reviewed the plates for the departure and arrival procedures. My aircraft is equipped with a Garmin 430W and we loaded the departure procedure and then the arrival procedure; however; we noticed that we lost the departure procedure in doing so. So; we went ahead made a cognitive decision to depart and fly heading 190 and to await instructions. In the process of departing the wind hit more violently than expected and I found myself flying heading 170. With rising terrain and flying in VMC I instinctively began flying a downwind departure as I've done dozens of times instead of sticking to the 190 procedure filed. The systems in the airplane operated perfectly in notifying me of rising terrain; as well as the controllers at Spokane Approach were quickly on the ball to ensure I was OK. I recognize the importance of following instructions and understanding exactly what I'm to do; for had this been in IMC conditions the outcome would've been very different. I sincerely apologize for my actions and take full responsibility for them.