As a general rule, discomfort that appears a day or two after you lift isn't cause for concern, especially if it's in the form of aches, as opposed to sharp pains. As I've gotten older (I'm 51) I've noticed that the sort of thing you describe has become more common. The more I focus on perfect form and not trying to grind out that final rep, no matter what, the less likely I am to have problems a day or two later. (I've abandoned having set number of reps in my workouts. Now I quit when I'm positive I can do one more rep with good form. Yes, it slows my progress a bit, but it's made a *big* difference in the post lifting ache & pains. The tradeoff has absolutely been worth it for me.)
Another good guideline is to move it if movement makes it feel better (moderately at first, especially after any injury). If movement makes it feel worse, either reduce the load until that doesn't happen, or don't move it that way.
Lots of people have had success by treating their "I am here" aches and pains with trigger point therapy. There's a lot of "bro-science" and outright quackery out there about trigger points, but I can recommend two very solid sources: painscience.com and the "Trigger Point Therapy Workbook" by Davies. Both have helped me out enormously for many years.