Wearing baby outward facing before 4-5months- need advice

My son is almost 3 months old and cries and screams and is generally  fussy if I don't hold him with his back against my chest, supporting his bottom and his chest and facing outward. He wants to be close but he wants to see everything that is going on all the time. I have an injured wrist already, so holding him like this for hours everyday is not helping it heal and makes it impossible to go on with life during the day. He has pretty good head and neck control. Suggestions or advice on if/how I could wear him?  (Ergo baby 360? Other wrap)