Since you want something with symmetric encryption, you probably already know PAKE protocols, e.g. SPEKE, which uses the classic DH with a low entropy password.
However, if you want to avoid PKC, you are very limited and you reduce overall security by a lot:
- You can use MACs, hash functions, symmetric encryption, etc. to generate longer pseudo random keys. However, both parties need to be able to execute the same steps and need the same data.
$\rightarrow$ Any nounce has to be communicated in some way, and should not be sent in plaintext.
$\rightarrow$ The entire construction relies on the low entropy password. There is no security gain.
Unfortunately, you need some structure preserving function to design a DH variant and the structures have to be sufficiently large. This ultimately leads back to public key crypto.
If you want to save space, you might want to think about using some kind of ECC-based DH key exchange.