I cannot advise about the midwife doing the clip, I am sorry! There are just too many variables. I think this is a case of, trust your instincts. I hope the info I linked can help you with understanding what is involved. Someone is always the first procedure for someone-you know? But if you would rather wait to see the ENT that is ok too.
I hope she can help with latch, but for some babies the tt really is a barrier that must be removed in order for nursing to be comfortable. If you cannot get a clip for a while, your choices woud be to keep nursing despite the pain and possible injury to you nipples, going back to using the sheild (maybe a different one) or temporarily pumping and bottle feeding. (or some combination of these.) All have risks and benefits.