I slipped in a puddle of water at a Target store on Saturday 29th.
At first just my arm, shoulder and neck hurt.Now I am having back spasams.
I called their head office and they said that I have to go to the
doctor on my own dime. What would you do?

It's very likely you spoke to a non managerial employee or maybe even
the wrong department.

If it were me, I could contact the head of their Risk Management department.

Here's a name, but I'm not sure how recent this article is.
http://www.findarticles.com/p/articles/mi_m0BJK/is_3_15/ai_114004917#continue

This is the department in charge of public safety.  The last thing
they want is a lawsuit on their hands.  Explain your situation and I
think they'll take care of your medical bills.  If not, consult with a
personal injury attorney to find out what your options are.

The General Counsel (chief in-house lawyer) for Target Corporation is
Timothy R. Bear.

His contact info. from the Hennepin County (Minnesota) Bar Association
is here: http://www.hcba.org/memlist.asp?display=lastname&id=1340

It doesn't hurt to start at the top.

Oops.  Make that Baer, not Bear.

Hopefully you filed an incident report in the store right after it
happened.  Also, why was there water there?  Was it raining outside
that day and it was tracked in, or did something spill in the store
that should have been cleaned up?  That will affect how determined
they are to help you.  If they had just mopped the floor or something,
what there any signs that said "Caution: Wet Floor"?  And, it is
probably right that they are going to make you go to the doctor and
have you pay for it and then if they are going to take care of it, you
will be reimbursed.  It's sort of like when you get in a car accident
- you get estimates and then you get the money.  For something like
this, it is probably hard to get estimates from doctors, so they would
more than likely go the reimbursement route.  Oh, and be persistent
with them, but not overly aggressive or unpleasant to deal with...that
will turn them off and reach for the "claim denied" stamp.  I'm not
suggesting inviting them to tea, but it's not wise to start your
conversation with "I'm gonna sue you for so much I'm gonna be your new
boss."  Good luck with your claim.

Let's see - stay home in pain and maybe it gets worse wating for
Target to pay OR go to the doctor and get help?  No brainer for me. 
I'd go to the doctor.  If you think you have a claim against Target
you can file it and get reimbursed later.

Thanks toall of you that commented on me falling at Target.
I have a doctor appointment on the 2nd.Nov.
I did file a incident report,I contacted the 800 number that was on
the incident report,not very helpful.
Nelson, thank you for the information on the lawyer.
clevegal42 to answer your question about why there was water on the
floor, the answer is I don't know. I live in Tucson so, no it was not
raining outside, I'm sure it had something to do with it being close
to the garden center?? And,thank-you for the advice to be nice.