In the beginning i pumped every 3 hours and i had engorgement if i waited longer. I massaged my breasts in a hot shower and massaged them during pumping to try to unblock any milk in breasts. But what really helped was pumping more often to avoid engorgement. I froze extra milk. At first i fed baby her bottle and then pumped for 7 or so minutes. It was sleep depriving but i tried sleeping during the day to make up for loss of sleep. Then i slowly started to go 5 hours during the night without pumping and my breasts got used to it. When you dont have problems with engorgement anymore you can slowly take a little longer to express and cut back on the amount of time you express. Keep up the great job!
Look up reverse pressure softening. It will safe you in those times you feel engorged. And it will soften you up so that it makes it easier to latch.
You didn't mention which pump you are using, but the quality of your pump makes a big difference in how much milk you get out in a session as well as how much time it takes a session to completely drain your breasts. Also, have you tried adjusting your suction and speed on the pump? More efficient pumping could cut down on the 45 min pump times.
I tried breastfeeding but just found it too painful. I'm happy with expressing. I've found that when my breasts do feel engorged I just express out by hand to relieve some of the pain.
My baby is 2 weeks today. At the beginning, she couldn't latch properly, it was so frustrating, she would cry, made want to give up but I was determined to make it work. In few days of trying, she successfully latch, I was so happy. Now I pump before I go to bed so I give her expressed bottle milk at night and I breastfeed her during the day. So my advice is don't give up, she is still so young, she can still learn how to latch. If you can't do on your own, ask for help from lactation consultants or nurses from the hospital or clinic. Trust me, it made my life easier by doing both breadfeeding & pumping.
I am not nursing baby as she doesn't latch on to my breasts. So I am bottle feeding her from my expressed milk and topping her up with formula milk if she needs it.
Your breasts make enough milk to satisfy baby. The more they are stimulated, the more they make. So if you are nursing baby AND pumping, your breasts think they have to make more milk. You may want to slowly decrease the times you pump and just strictly nurse baby until you don't feel the need to pump at all.