Blood test anxiety!

I have a debilitating fear of needles. There have been multiple times in my life when i have been pinned down in order to get a shot. Last night i tried to get my blood drawn and it was an absolute nightmare, and ended up not happening. I start my period next week so i was wondering (if anyone knows) can i just give them some of that blood instead? Also, how long is the needle in the skin and how long does the actual blood drawing part take? Any tips would be great.