Can I still upgrade?

Today while shopping I lost my phone, I don't know where. I have insurance with att, and I'm filing a claim. However November 20th, I have an upgrade and have been planning on using that for a new iPhone, with they still let me?

I upgrade yearly with Verizon, and I'm getting my iPhone X tomorrow!

Ask them since I do not know who THEY are

Yes, making an insurance claim does not change anything else. Your contract remains the same, your upgrade date remains the same, any amount you may owe on the lost phone remains the same. You will also pay (at least) $100 for the new phone as an insurance deductible.

I have had to make insurance claims on 2 phones, both through AT&T.

Ask THEM!

If your upgrade requires a trade-in, yes you'll need to follow through with the insurance claim and get a phone in your hands. And after that, you can take advantage of the upgrade. The fact that you just got the phone through insurance won't make a difference, you've been paying for it for (I presume) a year and a half already.