Yes, this is a False Widow spider and Steatoda nobilis is the species - looks like a juvenile. I feel that the fact it was up your shirt and hasn't bitten you should help to counter their 'deadly' reputation.
I feel that I was just lucky as I even touched it when it fell on the carpet as I didn't recognize it was a spider immediately... Probably if the spider didn't have an escape route available he would have turned against me. I'm glad it didn't hide in the hood and I was able to spot it.