Here is a small rant from me: If your statement about going to 17 doctors in 2 years is true, WHY???? You really are doing yourself a disservice, running from doctor to doctor. You need to find ONE doctor that you trust, and keep returning to him (or her) with new symptoms, or symptoms that return, to get answers.
Many diseases, some neurological in nature, some metabolic in nature, "look alike" from the outside. That is, have similar symptoms, behave in similar ways. It often takes time, and tracking a patient *over time*, to see what develops, to see if there are patterns of symptoms happening, to see if things change, or worsen, or sometimes improve at different times. If you go to doctor to doctor -- and 17 times! -- none of them have an opportunity to serve you well.
I know we're a society that wants "instant answers", and "quick fixes". By now surely you understand that whatever it is that is ailing you isn't going to be fixed quickly. And may not be fixed at all. You may have a chronic illness that is treatable, but not fixable. You're going to have to develop a huge "patience bank", and just wait and watch and see what happens over time.
I'm done with my rant. 
On to your questions.
Electric shocks: If you're experiencing L'ehermittes sign - -it's pretty common with MS (and other neurological disorders), it can present itself in a variety of ways. The shock usuall starts in the neck, and travels through the shoulder, sometimes down the back and butt, sometimes even down the legs. (You talk about it "down your spine" and others talk about it "down their back" - -I think they're talking about the same relative thing.) And it can occur in the arms. But you'd want to be sure that there isn't some sort of nerve compression happening in your neck that is causing it -- as that can cause the shocks if they primarily occur in your arms.
Purple spots on your legs: The doctor was correct to check for lupus, as that sometimes is an early sign. But if you've gone through all the testing, two things can be the result: You don't have lupus. Or you do, but it was too early to find it when you underwent that first testing. But given you've not described any other lupus-like symptoms here, perhaps the diagnosis of "not lupus" was correct. But again, this is one of those things that may develop *over time*, but if you've gone to other doctors since that first test, you'd have to be tested all over again.
Fatigue: Fatigue such as you describe is very common with MS (and with some other neurological problems.) There are some meds that help some people with it. Generally it is one of the main reasons why people end up having to quit their job, or greatly reduce their job or family expectations. It can creep up on you at unexpected times, too. And indeed, heat can cause it - -and other neurological symptoms, to worsen.
The shakiness: Could be related to MS. But it could ALSO be related to problems with your thyroid. Have you been tested for either an overactive or underactive thyroid? Or diabetes? (Which also can cause the purple discoloration in your legs). The drop or sudden rise in blood sugars can cause those kinds of problems.
Bladder problems: Are you certain that you've had *infections* several times a year -- or that you *think* you have an infection (because you can't pee normally), and so go to the doctor? Childbirth can affect a woman's bladder in negative ways. But you also could be experiencing a "neurogenic bladder" -- a bladder affected by your nervous system not operating properly. The common symptom is either an inability to pee, or a sense of having to pee immediately after having tried to do it, or bladder incontinence -- a sudden uncontrollable urge to pee, and you wet yourself. Or a combination thereof. The bladder isn't infected -- that is, when tests are run there is no infection -- just that it doesn't work properly.
Not having hot/cold sensations on one side: Well, obviously this is not "normal", or two doctors wouldn't have brought it to your attention! There is no "hallmark" of MS symptoms. It varies for each of us, and often in the same person. Some folks experience the loss of hot/cold sensation as numbness; others don't feel "numb", but also cannot sense temperature changes.
Increase in lesions: If indeed it is MS, then that's pretty typical. MS is a *progressive* disease, meaning it worsens over time. More lesions mean progression, or worsening.
NOTE though: there are lots of reasons for lesions to appear on an MRI. Again, a doctor likes to watch a patient over time, particularly one where a few lesions have appeared, and some symptoms. And then he'll do another MRI in 6 months or a year, and see if there is progression. This helps narrow the focus for him, and gets you closer to a diagnosis.
You state you've "never had diabetes" -- presumably one of those 17 doctors tested you for that? And you state you have "low blood pressure" -- have you ever taken your blood pressure when you've had those shaky episodes? That might be helpful information for your "new" neuro to know about.
Come back and let us know what the "new" neuro tells you, when you see him next.