Peas are traditionally planted "as early as the soil can be worked". Here in western Oregon, peas are planted from late February till about mid April for a May- June harvest. Peas don't like hot, dry weather. Planting now would probably be a mistake, unless you live in a place like Alaska that has cool summers. There is another window for peas in the fall, but not many people here plant them then.
Carrots are planted here in western Oregon from March till about mid- July. The seeds are hard to germinate when the weather gets hot, so I try to plant mine during a cool, wet period before June 1st. If it does gets sunny and warm, I water the bed 2-3 times a day and use cardboard sheeting to shade the bed and keep the surface moist. Carrots planted now will be ready for a fall/winter harvest. There is a also an overwintering variety in Oregon named Merida that can be planted in September when things cool off and the rains return, but not many folks plant this variety.
Here is a spring planting chart from Territorial Seed Company for Pacific Northwest gardeners:
https://territorialseed.com/blogs/spring-growing-guides/spring-growing-chart
Blake, please let us know where you live so we can be of more help. Good luck!