"Even my doctor said to me, 'You have small Tupperware, so I don't know how much milk you're gonna produce,' " Today's Dylan Dreyer recalls to PEOPLE

By Jen Juneau
July 03, 2017 04:00 PM

New mom Dylan Dreyer‘s first tussle with breastfeeding wasn’t quite what she’d expected it to be.

In an exclusive interview for PEOPLE’s Celeb Parents Get Real, the Today show meteorologist reveals the details behind her initial struggle to ensure her son Calvin Bradley, now 6 months, was getting enough nutrients.

“The first three months, Calvin was looking thin and svelte — he looked like a nice, fit little baby,” recalls Dreyer, 35. “We go to the doctor and the doctor says, ‘You’re really not feeding him enough food.’ I was exclusively breastfeeding. And he said, ‘[Calvin]’s getting about half of what he should get in a typical day.’ ”

She continues, “And it broke my heart. I cried when he said, ‘You have to supplement with formula,’ because I felt like I’d let him down and my body couldn’t do what Calvin needed me to do.”

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Although breastfeeding was a bit of a learning curve for the mom of one (who admits she was “scared to death about” it), she says she went in knowing it could be a challenge.

“Even my doctor said to me, ‘You have small Tupperware, so I don’t know how much milk you’re gonna produce for your baby,’ ” Dreyer says.

She adds, “Now we’ve worked in formula, and I’m still breastfeeding him — for whatever benefit that’s worth to him — and I’m proud of myself.”

That guilt Dreyer initially felt over being unable to breastfeed exclusively isn’t the only type she has endured as a new parent.

“There was one day I was really tired, really on edge, Calvin just kept crying and crying,” she remembers. “I felt myself getting angry and frustrated, and I handed him to [husband Brian Fichera] and I said, ‘You need to take him, because I’m in a bad place right now.’ ”

Dreyer continues, “It makes me feel so guilty for having to do that because I couldn’t handle it … [but] that’s why we’re a team, because I could hand [Calvin] off to [Brian].”

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Dreyer says “chaos is an understatement” when it comes to being a mom, but her job on the Today show gave her some now-much-appreciated practice in waking up before sunrise.

“Now it’s the balance of waking up for work, functioning on very little sleep and then going home and having to entertain a baby,” she explains of how her routine has changed.

“But I don’t care how miserable I am because I’m just tired and I just had an off day, but when I see Calvin smile, I just want to do everything to keep that smile going.”