私は日本語と英語で思っています。


Is this the proper way to say "I think in Japanese and English", or should I
be using a particle other than で?




The issue is in the verb choice, not in the particle. The **only** possible
particle is indeed で. If that is not used, the longer phrase 「～～を使って」 will
have to be used.

The verb to use here is 考える, not 思う. 思う is too passive in meaning.

Native speakers would say:

> 「（私は）日本語と英語で考えています。」 or
>
> 「（私は）日本語と英語の両方で考えています。」

