Postpartum hair appointment advice

It’s been over a year since I last had my hair done due to the pandemic and I’m in desperate need of a color/cut. I’m 4 weeks pp and I made an appointment when I’ll be 2 months pp because that’s when I’ll be officially fully vaccinated. My appointment is for a balayage and a trim. I just noticed, however, that my hair seems to be starting to fall out, so I’m wondering if maybe I should put my hair appointment off until after my hair is done falling out? The thing is, I don’t think my hair stopped falling out until around 6 months pp last time and I’m not sure if I can handle waiting that long lol. I’d also love a new fresh look for summer, especially since we’ve basically been quarantined this whole year and now we want to finally start seeing people again since we’re vaccinated. Help!?