You said, "TIAA and took it from my Fidelity IRA," which is impermissible if the TIAA account is truly a 403(b). Did you mean to say instead that your TIAA 403(b) RMD was taken from the Fidelity 403(b) along with the Fidelity 403(b)'s RMD?
If the distribution from the Fidelity 403(b) was sufficient to cover both the Fidelity 403(b) RMD and the TIAA 403(b) RMD, you don't have any problem there. If no distribution was made from the TIAA 403(b), you won't have any income from TIAA to report.
The RMD for your IRA(s) can can be aggregated and the total IRA RMDs can only be satisfied from your IRA(s). The the amount Form 1099-R with the IRS/SEP/SIMPLE box marked only applies to satisfying the RMD(s) for your IRA(s). Your RMDs for the 403(b) accounts can be aggregated and the total 403(b) RMDs can only be satisfied from your 403(b) in any combination. The amount on the Form 1099-R without the IRA/SEP/SIMPLE box marked only goes toward satisfying the RMD for the 403(b) accounts. If either Form 1099-R shows an amount less than the total RMD for that type of retirement account, you have an excess accumulation subject to a 50% excess accumulation penalty unless corrected and you request a waiver of the excess-accumulation penalty.
