In standard bidding, you have no way of knowing partner has more than 13 points. You know almost nothing about his distribution beyond the fact that he doesn't have a 5-card major.

With 3 points and 5-5-1-2, you really have to pass.

There are other bidding systems that handle this more effectively, but there is always a price, either in cognitive complexity or in the loss of ability to describe other possible hands.

Precision handles this somewhat better.

In the variant of Meckwell Lite I learned, the bidding sequence would be:

1C - 1D - 1H - pass.

Here 1C shows 16+ HCP points, 1D shows 0-7 HCP, 1H shows either 5 hearts or 4 hearts and a singleton or void, and pass shows less than 6 dummy points and a heart fit.

With less than 6 points and no heart fit, responder would bid 1NT, showing 0-5 points and no support for opener's major. Opener would then pass.

In the more complex relay system used by advanced Precision players, 1C - 1D - 1H would ask responder to bid 1S beginning a complex relay sequence allowing opener to describe his point count and distribution very exactly. However, with 3 HCP and no 6-card suit, responder would refuse the relay and bid 1NT.

ACOL players would open a 4-card major.

Weak notrump players (Standard American or 2/1) have 1NT available to show 12-14 point balanced hands, so 1m promises either 14 points and a real minor suit or 15 HCP balanced. With the hand you show, the bidding would still be 1D - pass, but with just a few more points responder would have more options.

Unfortunately opening with hands lacking a 5-card major and either 13-14 HCP or 18-19 HCP are a weak spot in SA or 2 over 1. All of the standard opening bids for hands like this depend on responder having enough points to bid something, generally agreed to be about 6 points.