Betahistine (Serc ) is prescribed for dizzines and vestibular problems. There is little research available on it, because it isnt marketed in USA where most of the research studies are conducted. Anecdotally it is quite widely used without apparent problems. Observe the nursing baby for signs of drowsiness/ poor feeding in case

This is the entry I made for Breastfeeding and Medication 2018

“Betahistine is prescribed for vertigo, tinnitus and hearing loss associated with Ménière’s disease. There is no data on the amount that passes into breastmilk . It is an analogue of histamine and is believed to work by improving the microcirculationn of the labarynth. Side effects are reported to include gastro-intestinal disturbances, headache,  pruritus and rashes. Prochlorperazine or cinnarazine would be the preferred to drug to treat dizziness. If betahistine use is perceived as essential the baby should be observed for drowsiness, GI disturbance and rash. There are no animal studies on use during lactation. Plasma levels of betahistine are very low. Plasma protein binding <5% (manufacturer SPC) Anecdotally it has been used without problems in breastfed babies “

See also https://www.e-lactancia.org/breastfeeding/betahistine/product/

Because of pharmacokinetic data it is likely excretion into breast milk, but though from very low plasma levels, usually below the detection threshold (100 pg/mL), so it is unlikely that the amount that could reach breast milk is significant.