What are TEC 3 pills? White, round and blank on the other side?

Do you mean Tylenol with Codeine #3 (acetaminophen and codeine)? a.k.a T3
I take these all the time for my migraines. However, a pamphlet in the doctor's office said that even though T3's are best for migraines, I should also take a gravol for the possibility of feeling nauseous.

Codeine is an opioid pain medication. An opioid is sometimes called a narcotic. Acetaminophen is a less potent pain reliever that increases the effects of codeine.

Acetaminophen and codeine is a combination medicine used to relieve moderate to severe pain.

Acetaminophen and codeine may also be used for other purposes not listed in this medication guide.

Generic Name: Codeine, Acetaminophen, Caffeine
Strength: 30 mg, 300 mg, 15 mg
Manufacturer: Ratiopharm, Canada
Trade Name: ratio-Lenoltec No. 3
Type: Analgesic
Class: RX, CDSA I

I searched multiple databases for humans and dogs and supplements and couldn't identify your pill.