Do you have a cardiologist or neurologist who is treating you for your POTS? There is a significant subset of POTS patients that do have a rise in BP in upright postures. (It is actually a myth that orthostatic hypotension is part of the POTS diagnosis; see here:
http://www.medhelp.org/health_pages/Neurological-Disorders/Dysautonomia--POTS-Diagnostic-Criteria/show/1011?cid=196 ) There are different treatments that can be targeted to your particular case of POTS, including this aspect. What treatments/medications are you taking now and how are/aren't they working (including side effects)? What have you tried in the past and how did/didn't that work?
A Mayo clinic website states POTS "is the most common form of orthostatic intolerance without associated orthostatic hypotension."
You might see if your doctor is willing to do a laying and a standing norepinephrine level on you to see if you have the hyperadrenergic form of POTS. My own blood pressure goes up after a short bit of standing. I have never had this testing of laying and standing norepinephrine, but I have had my norepinephrine and normetanephrine levels be elevated above normal range before. I think I have the hyperadrenergic form of POTS. My heart rate when I stand up without sitting first after I have been in bed at night this year on a holter monitor would go up in the 140s to its peak level in the 150s. The year I was diagnosed with POTS (2004), I was iron deficient and my heart rate was going as high as the 160s.
I haven't really found much help for this increase in blood pressure problem (tried verapamil), but what I can say is if it is at all possible, don't give up on walking, even if it slow walking, because deconditioning can just exacerbate the problem, I believe.