The skin on my nose has large, clogged pores. What's a good skin care regimen to fix this? Retin-a is too harsh (red and irritated skin).

Dilute retina. Use retina every day or use moisturizer first to dilute strength of weakest retina .05. Salicylic acid products will also work to open pores. Other options although temporary are bier strips, or cllarisonic device available at drug store or sephora.Phtodynamic therapy can shrink pores rather than just remove debris.
Benzoyl peroxide. There are many acne medications that contain benzoyl peroxide that are over the counter. Don't put on too much becauses irritation develops and people may think they're allergic and not use it. Sparingly applied benzoyl peroxide can help unclog the pores. Be careful, it may permanently ruin towels and linen by bleacing so wash your fingers after application and don't wipe your nose with a towel.
Gentle cleanser. Wash with a gentle cleanser and warm water. Avoid scrubbing your face and using hot water, which irritates your skin more. Other meds like Adapalene or antibiotic gel/solution may be more friendly to your skin. Try warm compresses or steaming your face, then using blackhead extractor/strips for removing big blackheads. Good luck.