On the first visit you'd use a -25 on the E/M if decision was made at that time to proceed with it (decision for surgery). (99213-25, 20610, J1030). If the patient was told to come back for just the injection and no other (above and beyond) eval was done, then yes, only the injection/meds codes. Now if the doc evaluates a different injury/illness at the same time of the second injection that has nothing to do with the dx/injection on the second visit, then -24 would apply.
No, a 24 modifier would not apply in the scenario you gave. If the patient came to the office for a f/u knee injection and then also told the provider that his shoulder was bothering him and the provider evaluated the shoulder then you would bill the E/M with a 25 modifier linked to the diagnosis for the shoulder problem and then linked the injection and drug to the knee diagnosis.
24 mod is for an unrelated visit while the patient is in a GLOBAL period. Injections don't have a global period.