Sounds like your saddle is too narrow for you ... or possibly too wedge-shaped and forcing you onto the narrow nose even if the rear is wide enough.

Have you read the saddle threads? Start here. Unfortunately there's still a lot of trial and error involved in finding the right saddle for you, but knowing what size and general shape you need will narrow your choices quite a bit. See if you can find a shop that will let you test ride various saddles. Sometimes you'll know right away if a saddle is not going to work for you, but knowing whether it's really right typically takes at least one or two long rides.

If you're having trouble with your hands, that's likely to be at least in part a fit issue as well. Hopefully someone more knowledgeable than myself can chime in there ... I'm pretty comfortable with fit solutions to leg and knee issues, but upper body fit is still pretty much trial and error to me. Core strength plays a part, but so does handlebar bend, stem length and angle, lever placement, etc., etc., etc..... Definitely wear gloves if you aren't already - gloves are safety equipment more than anything else, ask anyone who's ever taken the skin off their palms - and you can get cushion from gloves as well as from spongier handlebar tape - but just like with your other contact points (saddle and pedals), fit first, then accommodation.

Welcome and enjoy!