Its not summer yet and I haven't been outside. I keep getting these small dark brown/black dots and spots all over my body. Are they new moles?

Yes. As we age many of us get spots as you describe. They are likely harmless but you should be checked by your pcp to be sure. Sun with the uv rays cause pigmentation to brown us up. Those uv rays can play havoc with moles. Moles that are new or existing can be transformed into malignancy so any mole changing character need immediate exam by your pcp and maybey referral.