Will phimosis cause a lot of pain during sex?

Maybe: It can if the phimosis is significant.

Depends: I you have a severely tight phimosis and the head of the penis cannot protrude past the foreskin or if the skin retracts but cannot go back over the head, then you may well have problems. If the skin is moderately snug, but is painless and moves back/forth without pain in a normal setting, it is less likely to cause problems with intercourse.

Most are okay...: Most of patients with phimosis would not be bothered - no pain - during coitus until the infection / inflammation (balanitis, balamoposthitis) kicks in periodically. Once balanoposthtitis happens and it tends to recur and worsen over time. So, if recurring despite topical care, circumcision should be done for long-term benefit.