This med isn't usually used as a first-line anxiety med (this is per my own research and my psychiatrist, who is a psychopharmacologist). When it does help it's usually because depression is a big factor. The reason is that this med is intentionally stimulating, and that's what you're most likely feeling. This might go away, so it's too soon to say it will last, but I would say, if this lasts, this drug is best stopped sooner than later if you don't find it's the right one for you. But any antidepressant can have start-up side effects that go away, you can't know that until you've been on it for a few weeks. I don't know about the tingles, but if they started when you started the med, same thing. This drug affects two brain neurotransmitters, norepinephrine, which is a stimulant and can make many people anxious, and serotonin, which besides working in the brain also has a role in digestion and in relaxing the muscles. Since you've started it, I guess I'd see what happens, but most people start on ssris, not snris, for anxiety for this reason. But you never know until you try. Hope it all works out.
There are start up side effects when you begin this type of medication and I'd guess this is the case here. Your doctor selected it for you and he has probably prescribed it with success. Some do use Effexor as a first line treatment for anxiety. https://mentalhealthdaily.com/2016/01/12/effexor-venlafaxine-for-anxiety-disorders/ Don't be discouraged or think it is the wrong choice necessarily. They have the multiple experience of many patients to base decisions on. :>) If the tingles are manageable, I'd try to weather it out for 6 to 8 weeks. If it is a transient side effect or start up side effect, it should go away. Our bodies get used to the med and the side effects of starting it then become less and some go all the way away. Some new ones may show up though that don't go away. Each person and the way they react are different. If the side effect becomes too much, then call your doctor. But my guess is that this will get better.
What else are you doing for your anxiety? Do you see a therapist? That can be very helpful for working on coping skills and working on eliminating triggers if possible. And all the lifestyle things like eating well, getting proper rest and exercise are very beneficial to the big picture of treating anxiety. Things like meditation and deep breathing, mental imagery, etc. can be helpful too. Hope it gets better soon!