how can i tell if i’ve injured myself or if it’s the typical exercise pain

By seeing your doctor. That's how...

Psycho's advice is correct, really ideal.

Since you don't want to take it, some rules of thumb (that are not nearly as accurate): Sharp, very localized pains are more likely to be injury. Broader-area, kind of pressure-sensitive achy discomforts are more likely to be sore muscles. If the pain level changes quite a bit with particular types of body movements (like you get a sharp stab or spasm when you move or something), more likely to be injury. If impairing normal body movement or activity (by something other than mild stiffness), more likely to be injury.

If something hurts, that's a decent reason to take some extra time off, and rest (or do a non-aggravating exercise). You have the whole rest of your life to be active, and improve strength/fitness. Resting to wait out an uncertain-source pain just costs a few days in the short run, no big deal. If you aggravate an actual injury, you might have to take weeks off from working out, or in a worst-case scenario, cause a life-long physical problem (though that's not super common).

The best advice, if not sure, is "see the doctor". Second best: Take some rest days, until you're sure it's not an injury.

Give it 3-4 days of COMPLETE rest.

If the pain/discomfort doesn't go away or diminsh by then, it's probably something more than DOMS and you should make an appt w/an orthopedic specialist.

Take it from someone who has had 2 rotator cuffs tears, a 3 way ligament knee tear, a sprained S-I joint, a chronic elbow deterioration, broken clavicle, broken ankle and a painful foot neuroma.