I would imagine your soreness in right hand is from the interval stretch of m6, p5 and M3 in Linus and Lucy.
That can be tough if you haven't worked on things to open up your hand which I would suggest taking slow to prevent injury. Simple one octave arppegios in Major, minor and diminished. Also parellel harmonic 3rd, 4th intervals.
Might want to massage your hands and fingers before and after.
Go easy. Then try holding down the L and L intervals and relax.