I have red dots under my skin on my upper lip area after microneedling. Did capillaries break?

blood vessels can be damaged and take vascular lasers and proper skin care to heal. 
I suggest a combination approach of :

1) skin care with products and PRP/microneedling
2) PDT light therapy few times a month with growth factors
3) laser treatments like clear and brilliant regularly and a few times a year Fraxel, Viva, Co2/Erbium
4) Sculptra injections a few times a year for collagen production with fillers like juvederm/restylane/belotero/radiesse/bellafill
5) thermage/ultherapy for yearly skin tightening with or without PDO or cone based instalift threads for lifting
6) botox every 2-3 months to stop movement lines and prevent lines at rest
7) deep microneedling RF like Fractora/morpheus8 for tightening of the skin
Best, Dr. Emer.

Great question. This pinpoint bleeding is very normal and is actually expected from microneedling. What pinpoint bleeding means is your therapist is treating the deeper layers that stimulate collagen & elastin growth. Redness & pinpoint bleeding means you have received a great treatment done by a skilled therapist.