Can taking Alprazolam, Atenolol and Terazosin cause bouts of diarhea or interfere with sleep?

Alprazolan is a benzodiazepine and is usually used for treating anxiety and panic disorders.

Atenolol is in a group of drugs called beta-blockers. Beta-blockers affect the heart and circulation (blood flow through arteries and veins).
Atenolol is used to treat angina (chest pain) and hypertension (high blood pressure). It is also used to treat or prevent heart attack.

Terazosin is in a group of drugs called alpha-adrenergic blockers. It causes the blood vessels (veins and arteries) to relax and expand, improving blood flow.
Terazosin is used for treating high blood pressure and treating signs and symptoms of benign prostatic hyperplasia (BPH).

All these medicines have side-effects and have the potential to interact with each other to produce adverse effects.

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After searching the literature I have found no significant drug interactions with the medicines you are taking.
However, it is worth noting that Beta-blockers (Atenolol) are associated with sleep disturbances and nightmares and also gastric upset including diarrhoea.

I think it is well worth discussing these symptoms with your Doctor. It could be that the Atenolol is giving you diarrhoea and interfering with your sleep.