Angry Teething

So we believe our 4 month old just started teething (possibly both bottom) about maybe a week ago and I noticed that if we don’t give him a teether toy for the most part he’s fine but sometimes he does get fussy and we just give him one to hopefully chill him out a bit but it seems like it makes it worse like the more he chews the harder he’ll chew and the more aggressive he’ll get with it and he’ll get frantic and not put the “right” part of the toy he wants in his mouth and eventually he’ll just BLOW and scream as hard as he possibly can (he got both of me and my husbands tempers when we were kids 🤦‍♀️) and the only ways I can calm him down is to pick him up and pat him and then feed him (I exclusively breastfeed him) and then he’s fine or to rub his gums with my finger. He’s very picky with his teething toys if he likes any at all and I’ve even tried the teethers you can freeze or refrigerate since I’ve heard so much good about them. He’s not on solids yet and he’s not big on pacifiers. I don’t know what to do because I want him to be able to soothe his gum pain but doing so makes him so extremely upset.