You can try, and it is worth the call. But going in with the right approach makes all the difference in whether you get a helpful response or a polite no.
Counselors and unit staff at county detention facilities are not technically required to pass along personal messages or phone number updates from outside parties. That is not their official role. However, many staff members are genuinely willing to help when someone calls with a reasonable, humble request and treats them with basic courtesy. The operative word is humble.
When you call, ask to speak with the counselor or case manager assigned to your son's unit, not just whoever answers the general line. Introduce yourself, explain that you are his parent, that your phone number has changed, and that you are hoping they might be able to pass the new number along so he can update his approved call list. Keep it brief, be gracious, and thank them regardless of the outcome.
If the counselor is willing to help, great. If they cannot or will not, the more reliable alternative is to send your son a letter with the new number written clearly inside. That gets the information directly to him without depending on staff to relay it, and InmateAid can send that letter today so it arrives within a few days. Once he has the new number he can submit it through the facility's phone carrier to update his approved list.
Either way, getting that number to him quickly matters since he may be trying to reach you and not getting through. The letter is the backup plan if the call does not work out.