Are There Any Antidepressants That Don't Have the Side Effect of Excessive Sweating?

Nerve-blocking medications. Some oral medications block the chemicals that permit certain nerves to communicate with each other. This can reduce sweating in some people. Possible side effects include dry mouth, blurred vision and bladder problems.
Antidepressants. Some medications used for depression can also decrease sweating. In addition, they may help decrease the anxiety that worsens the hyperhidrosis.
Botulinum toxin injections. Treatment with botulinum toxin (Botox, Myobloc, others) temporarily blocks the nerves that cause sweating. Your skin will be iced or anesthetized first. Each affected area of your body will need several injections. The effects last six to 12 months, and then the treatment needs to be repeated. This treatment can be painful, and some people experience temporary muscle weakness in the treated area."
"Peripherally, the anticholinergic agent benztropine reduced or eliminated diaphoresis at doses ranging from 0.5 mg every other day to 1 mg/d.2,3 Dry mouth was the only reported side effect.

Centrally acting serotonin antagonists may decrease diaphoresis through the 5-HT2A receptor, which signals the hypothalamus to raise body temperature. Cyproheptadine is an antihistamine with serotonin receptor antagonism. In case reports, it reduced or eliminated sweating in doses of 4 mg once or twice daily.4 Mild sedation was the only noted adverse effect. The norepinephrine and serotonin antagonist mirtazapine reduced diaphoresis within 2 weeks of initiation at 15 mg/d with no adverse effects.5 Sweating resolved after mirtazapine was titrated to 60 mg/d."

Not all the best of options but for those folks who need to be on (and maybe stay on) an effective antidepressant/anxiolytic that works well for them they may be worth investigating.

The strange thing is that it's not so much outside or in hot weather. It's whenEVER I go inside a building that doesn't have crosscurrents of air. The stiller the air, the worse it is. Museums, stores of any kind, have me soaked within minutes. It's not only embarrassing to be soaked & dripping when it's 65° in a store, i feel so hot in the core of my body that I feel ill, as if I were having sunstroke. It doesn't feel anything like hot sun on skin, it's like a furnace inside.
Once I get out of the building, I continue to sweat for another hour.
Exertion brings it on as well, like vacuming, etc. But inside closed buildings, it's so bad I really cannot shop or browse bookstores for more than 5 minutes before the torrent begins. Awful!!