Is there a surgical way to move the breasts and nipples closer together without implants?

Dear heyyyoThe angle that the breast lays on the chest wall can be changed with differential fat grafting. Moderate improvement in the direction your nipples point and the way your breasts mound sit on your chest can be achieved. The effectiveness depends of multiple factors. Consultation with experienced plastic surgeon  will help you see if you are a candidate based on the benefits and limitations. see more than one surgeon in consultation so you can make a well informed decision.

Thank you for your question.  In short, I will say "no".  Your nipples are supposed to be about 20 degrees divergent from the midline.  They should not be pointing straight forward.  Also, they need to be centered on the breast mound.  Generally, this is almost always true.  Some women to have breasts which are wider, which is just part of who you are and how you are made.  

and to find out what your options are, you should visit a local plastic surgeon for a consultation and to see what options are available to you.  Fat grafting can certainly fill deficient areas.  Nipple lifts or movements can be done with variations of the Benelli mastopexy.  If you want objective information from sites  such as this one, photos are mandatory.

Unfortunately you did not post any photo. "Pectus Excavatum" usually makes the nipples look to the middle of the chest,  while the "Keel Chest" makes them point laterally.The rule is that the Nipple-Areolar Complex have to be in the middle of the major projection of the breast.There is a vertical line that comes from the middle of the clavicle and passed thru the middle of the breast and is not possible to relocate the Nipple-Areolar Complex outside this line. The visual effect of this will look excentrical  an un aesthetic.The probable technical correction will be to use implants and move the Nipple-Areolar Complex to a more medial projection.

Pectus excavatum is not an uncommon issue. There are varying degrees of this condition, yours should be made less noticeable by the augmentation procedure, although this is based on your description and without photos. Having a more round "barrel-shaped" chest can cause the nipple position to point towards the sides. Some degree of change can be achieved through various surgical techniques, however they may not be positioned directly forward. 

The answer to your question would depend on your anatomy and without an exam or good medical quality front and side photos we would not know what suggestions might be appropriate.