(CBS News) – The nation’s most restrictive abortion law is forcing people to flee Texas in search of clinics elsewhere — and some of those clinics say they can barely meet the new demand.

CBS News had rare access to a facility in Denver, where nearly half the patients are from Texas. The Texas law, which took effect three weeks ago, bans 84% of abortions, according to the Guttmacher Institute. People more than six weeks pregnant now have to cross state lines to get an abortion.

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Dr. Rebecca Cohen, the medical director of the family planning clinic in Colorado, said the clinic has never seen an influx like this. Colorado does not have a state-mandated waiting period for the procedure.

“We haven’t seen numbers like this ever,” Cohen said. “An abortion can be painful. People can hurt. But this is different. We are seeing patients who are traumatized when they arrive.”

A patient at the clinic, who asked CBS News to conceal her identity, said she cried when she found out she could not get the procedure in Texas.

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“I cried all the way from when they told me through the counselor session,” she said. “I didn’t know what I was going to do.”

She’s a 34-year-old mother of three, who learned she was pregnant one day before the ban was enacted. She said she has an irregular heartbeat, which could make the pregnancy risky. She made the 1,600-mile roundtrip in one day, using money she’d saved for a family vacation to pay for her flights and the procedure.

“After the procedure, you’re supposed to take it easy. I’m not going to get that option because I’m going to have to walk through the airport and everything else to get back home,” she said.

Hope Medical Group in Shreveport, Louisiana, is just 20 miles from the Texas border. Even with a 24-hour state-mandated waiting period, appointments are hard to come by. At one point, there was a five-week wait for an appointment.

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“Women should not be going through this. It’s unconscionable,” said Kathaleen Pittman, who runs the clinic. “They’re literally begging to get in and be seen as quickly as possible.”