I felt very much like you OP - more worried about the epidural!
What happened in fact was the first labour became overwhelming very quickly. I had booked a home birth and the first midwife who came out was useless, she was really unsympathetic and said "I'll not give you gas and air now, if you have it now you'll end up with an epidural!" I had thought gas and air was a more "mild" pain killer.
Luckily she went away and the second midwife was excellent, she recognised I was going into panic and helped me to take back control and calm down. It is important to have some kind of technique to come back down if you are spiralling. I recommend reading Juju Sundin's Birth Skills, (and take notes so your birth partner can remind you), this is full of such gems.
The birth went well from then on.
Second labour was ten years later, I felt falsely confident, again once it started ramping up it became overwhelming but this time nobody talked me down. I tried getting in the pool as that had helped with DC1, but it didn't help this time. The midwives said I still had ages to go so I thought screw this, I'll try the epidural, it can't be that bad.
Well, I was panicking the whole way through them doing it. Kept freaking out that they would slip and I would be paralysed. Or I'd get the insane headache thing. Was so scared that I couldn't sit still through the contractions (and actually struggled to) but did manage it, it was OK.
However, the epidural didn't work!
Third baby, I thought about epidural but ultimately I felt I didn't want to go through all the faff of getting it put in if I could cope with the pain, and I did manage to cope much better (Juju's tips served me best in this one) so I didn't have any pain relief except for getting in the pool, which did help this time, and gas and air at the very end.