Hot take: I train ON injection day and the day after, deliberately. My reasoning is that mild nausea doesn't affect my lifting performance — it's uncomfortable but I can still squat. And exercise actually seems to reduce my nausea. Something about blood flow or endorphins, I dunno.
Not saying this would work for everyone but don't automatically assume injection days are write-offs. Try a light session and see how you feel. You might surprise yourself.