I began road biking about 9 months ago on a mens GT fury road bike that was given to me free and was about 20 years old. I got very sore upper arms from riding it and now I have a new bike, its a medium sized mens road bike(I didnt like any of the ladies ones and the guys in the bike shop assured me it fitted me well ) So I have has this bike for about 2 weeks and after about 30mins of riding I still get sore anterior delts from riding with my hands on the hoods severe burning pain that stops as soon as I sit up or stop riding. I thought it qould go away with time but after this long of daily riding it cant be simply a strength issue. So I took the bikw back in and they gave me a different stem that brang my hands closer in towards me so that I wasnt stretching as far and brought me higher up too.. STILL GETTING SORE FRONT UPPER ARMS AND NOW A SORE MIDDLE BACK. Although maybe my back muscles arw just weak. Its the muscles right down by my bra strap.
Its too late to take the bike back now so I need to fix it and obviously the people at my local bike shop are CRAP at fitting bikes.
What to do?

It is difficult to say what your best course of action ought to be. If the bike is actually correctly sized for you, then is is a matter of adjusting the fit. It the bike is the wrong size, no adjustment is likely to improve comfort by much. If you could post several photos of you on the bike, it would provide the best way to see if the bike is your size.

Hit the Gym .. strengthen those Muscles to support you Better ..

Sight Unseen that is the best I can suggest ..

take more measurements and data specs on the frame geometry and component dimensions ..
And the arm length Torso length , leg length Etc. and report back ..

the number crunchers need numbers ..

Complaining in text works well, Solutions with out real information is harder to pull Off..

It's really weird how so many folks, who should know better, think that upper body problems can be solved by putting the rider more upright. Usually the opposite is the case. Be that as it may, here are some photos of women on bikes showing about what it's supposed to look like. You can just look at the women and ignore the hands:
https://www.bikeforums.net/road-cycli...l#post12953035

But even with your fit issues sorted, my guess is that you still need upper body weight work to make your shoulders stronger. I ride a lot, but every winter I do a few months of weight work at the gym prophylactically.

I do the following, supersetting them for 12 reps. IOW I do the first, immediately the second, immediately the third, then repeat 12 times. If you don't have a gym or dumbells, start with canned goods, either one can or cans in a couple of bags.
Dumbbell Lateral Raise
Dumbbell Rear Lateral Raise
Dumbbell Alternating Front Raise

Following up on cfboy's post, here is Lizzie Armistead (World Champion) in full flight.

Lizzie eyes multi-medal games glory | Olympic Games 2016 | Sporting Life

See how her upper arms are close to 90 degrees to her spine, which supports her with the least effort from her arms.

The bend in the lower spine will be rather individual, depends on the person's flexibility and anatomy.

And here she is, gutting it out in pissing rain. Tough cookie.

Lizzie Armitstead Interview: ?I?m a road cyclist in my own right?

See how her arms are roughly parallel to each other.

Given the location of the original pain, I would look at whether the bars may be too wide. The hoods should be roughly as far apart as your shoulder width. (There is some individual variation. Sprinters may use wider bars, for more leverage as they throw the bike from side to side.)

As this is a man's bike, and men's shoulders are usually wider than women's, I'm going to guess you may want to try a narrower bar.

The new upper/mid back pain may mean that the shorter stem now has you too "scrunched up", forced to bend your back too much. I would try going back to the original stem. But only make one change at a time.

Photos would be helpful, but that's what I can think of, sight unseen.

I don't want to discount the importance of upper body and core strength, but that degree of pain in just 30 minutes, when your previous bike didn't hurt you, suggests there is (also?) a fit problem.

Sore hands, wrists, shoulders, back, all within 30 minutes... sounds like me when I first started riding a road bike, and I'm a dude. When there isn't enough core strength to hold the upper body up, that weight goes onto the hands. The other part is that with an aggressive fit, the rider is expected to ride hard most of the time, which takes weight off the hands. It's remarkable how my main road bike goes from feeling wonderful to hurt-y if I take it on a slow ride.

Yep, perfect fit, great form. Note her hand position on the hoods in the first photo. That's my going fast now hand position except that I hook my little finger behind the bars for more safety.

You may want to give this a read How to Fit a Bicycle
It is a common sense approach to fitting your bike. You will feel some soreness getting acclimated to your bike but it shouldn't be inflicting pain on you.