I assume you are boxing without kicks.
Try changing the way you hold yer hands if you are getting hit by hooks/haymakers. The traditional MT style "peekaboo" hand posistion allows you to protect your head very well from both kicks and hooks/elbows etc.
It is fairly easy to slip one hand back over the temple area in time, this will block most hay makers and even good hooks. (for kicks it is best to use both hands if possible, one at the temple one to parry. Then you can parry or even trap the kick as well. For protection from elbows the forearms cross horizontialy over the face )
Work on slipping, even just a simple turn of the head will allow you to take or slip the punch and stay inside too counter punch. Slipping and ducking the punch and hitting the body might work, a good body shot can K.O.
Parrying a haymaker is very effective, the guy likely is already off balance from too much torque any way, a little extra push might spin him right around even giveing you his back or causeing him to fall.
(in MT the classic parry is usually done vs a jab, then followed instantly by a very good clean leg kick, or even a head kick that is very hard to see comeing as it strikes the rear of the head)
Mitakuye Oyasin "We are all related"