First, you should find a spiritual director, who can also help. Ask your pastor if he knows of an (lower-case o) orthodox spiritual director in your area. But, in the meantime:
If you want to be effective at spreading the faith, take a look at the Daughters of St. Paul. cmswr.org/member_communities/DSP.htm .
Many of them don’t particularly run around much, but I know some of them travel regularly, giving conferences and lectures and the like. Take this road if you want to be an effective voice for the truths of the Church, and (if you’re going to college, or whether they might train you) make sure you undertake the study of classical rhetoric, a second modern language, Latin, the Church Fathers, Dogmatics, and Aquinas/Aristotlean philosophy.
If you want something more personal, one of several hospital orders would be better: many people pass through hospitals at difficult times in their lives: reaching different people is more important than being in different places.
If you have a spirit of activism, rather than one of Evangelism, you could try the peace corps or the ccservicecorps.org/, or there are a few other lay missionary organizations, until you are over it.
If you’re really just interested in the exotic, go check out Mother Theresa’s Missionaries of Charity - you will meet more people than you ever could dream of - and, again, is it really more important to physically run around than to touch many lives?
Simply put, there are no, and as far as I know never have been, primarily mendicant/itinerant orders for women because no ordinary will permit the heightened risk of them being raped or murdered. Or worse.
No, it’ s not fair. But, we all have to sublimate even our good desires into something more perfect.
Finally, the reality is that, while you’re young and travelling a lot looks good to you - and I encourage it - but (speaking as one who has traveled extensively) as you get older it will become less important. Specifically, you will probably want to nest: all women have a mothering instinct just as all men have an instinct to be fathers, and while brothers, priests, sisters and nuns give up having natural children for the sake of the Kingdom, it is usually disordered to NOT have some kind of a close-knit, spiritual family - to ‘settle down’.
Anyway - the important thing about all of these orders is obedience. I know it sounds difficult to our modern ears, but obedience to your ordinary/superior is what produces greater fruit (and consequently greater fulfillment) than you could ever do by yourself. In any vocation, it is by the cross of obedience that you will become holy and merit heaven, bringing all good gifts of God to those you are given to love.
Know you are in my prayers.
[p.s. just noticed the nursing suggestion above, and can affirm that is probably true, but I don’t know of any orders that run around a lot like that]