Is it possible to encrypt data points but still be able to select the ones "near" a given value?
No, a cryptosystem can't do what's asked.

Proof: if one can precisely answer queries of the form "how many data points up to a distance of $3$ starting from an origin point = $n$" (a subset of what's wanted) for any value of $n$ with $|n|\le m+3$, and each point has integer value $v$ with $|v|\le m$, then one can find exactly the value of all the points in the set with at most $2m+1$ queries (with $n$ going from $m+3$ down to $-m+3$, each revealing if $v=n-3$ belongs to the set).

Thus in order to make the problem in the question tractable, one must use much larger integers (so that the necessary number of queries or work becomes infeasible), or/and heavily limit the number of queries an adversary can make, or/and introduce some fuzziness in the answers, or/and (as pointed by otus in comment) introduce the notion that some of the query is sent somewhat "enciphered" to the holder of the database. And it might well be that no practical system is possible.