No - I would hold off on the injection only because if it is just a sprain I'd think it would respond to the rimadyl (Which is an non-steroidal antiinflammatory like advil or tylenol). Not sure what she wanted to inject. I don't really think it would hurt, but I don't know. There's a lot we don't know about SM - and I assume that is your concern w/ not wanting the injection in the neck?
If I thought it would make a difference for her and her recovery I'd say do it. But i sounds like she is not responding to the Rimadyl and if it were just a sprain, I think she would. So I think the next step is an x=ray to see if there is more going on there.
Dogs are not our whole life, but they make our lives whole.