There are two separate questions here about the meaning of different verbs.

John 1:3c γίνομαι

The operative verb in John 1:3 is γίνομαι (ginomai), which according to BDAG means the following:

1. to come into being through process of birth or natural production, be born, be produced, eg, John 8:58, Rom 1:3, Gal 4:4, 1 Cor 15:37, Matt 21:19.
2. to come into existence, be made, be created, be manufactured, be performed, eg, John 1:3, Heb 11;3, Acts 19:26, Matt 11:20, 23, Luke 10:13, Acts 8:13, 4:22, 2:43, 30, 12:9, 24:2, 14:3, Mark 6:2, etc.
3. come into being as an event or phenomenon from a point in origin, arise, come about, develop, eg, John 12;29, Rev 8:5, 11:19, Matt 8:26, Mark 4:39, Luke 8:24, etc.
4. to occur as process or result, happen, turn out, take place, eg, Matt 1:22, 26;56, etc, etc, etc
5. to experience a change in nature and so indicate entry into a new condition, become something, eg, Matt 5:45, Mark 1;17, Luke 6:16, 23:12, etc.

Thus, it is clear that "create" is entirely consistent with the meaning of γίνομαι (ginomai), especially in John 1:3.

Col 1:16, κτίζω

The verb κτίζω (ktizó) occurs twice in Col 1:16 and is used in the following senses in this verse:

• in "Him" (The Son, Jesus) all things were created
• via Him all things were created
• for Him all things were created.

BDAG defines this word as, "to bring something into existence, create"

The real crux of this verse is the meaning of the preposition "en" (the second word in the verse of the Greek text). This is an extremely versatile word that has, according to BDAG, 12 meanings and uses plus several sub-meanings and uses. While this is too much to reproduce here, the relevant meaning is: 3. marker of close association within a limit, in, eg, Col 1:16, meaning "everything created in close association with him".

Note that this verse is actually saying that:

• Jesus created all things in association with God
• Jesus created all things through His power
• all things were created for the benefit of Jesus

Note that V17 adds a further dimension of saying that not only did Jesus create all things, that He also sustains/maintains things as well.

Thus, this verse is teaching that Jesus created all things in close association with the entire Godhead as Gen 1:1, 2 suggests.

Note the comments of Meyer:

ἐν αὐτῷ is not equivalent to διʼ αὐτοῦ (Chrysostom, Oecumenius, Theophylact, Erasmus, Beza, Bleek, and many others), but: on Christ depended (causally) the act of creation, so that the latter was not done independently of Him—in a causal connection apart from Him—but it had in Him the ground essentially conditioning it. In Him lay, in fact, the potency of life, from which God made the work of creation proceed, inasmuch as He was the personal principle of the divine self-revelation, and therewith the accomplisher of the divine idea of the world.

Ellicott is also helpful:

(16) For by him . . . all things were created by (through) him, and for (to) him.—Carrying out the idea of the preceding clause with accumulated emphasis, St. Paul speaks of all creation as having taken place “by Him,” “through Him,” and “for Him.” Now we note that in Romans 11:36, St. Paul, in a burst of adoration, declares of the Father that “from Him, and through Him, and to Him are all things;” and in Hebrews 2:10 the Father is spoken of as One “by whom are all things, and for whom are all things” (the word “for whom” being different from the word so rendered here, but virtually equivalent to it). Hence we observe that the Apostle here takes up a phrase belonging only to Godhead and usually applied to the Father, and distinctly applies it to Christ, but with the significant change of “from whom” into “in whom.” The usual language of holy Scripture as to the Father is “from whom,” and as to the Son “through whom,” are all things. Thus we have in Hebrews 1:2, “through whom He made the world;” and in John 1:3-10, “All things were made”—“the world was made”—“through Him.” Here, however, St. Paul twice adds “in whom,” just as he had used “in whom” of God in his sermon at Athens (Acts 17:28), probably conveying the idea, foreshadowed in the Old Testament description of the divine “Wisdom,” that in His divine mind lay the germ of the creative design and work. and indirectly condemning by anticipation the fancy of incipient Gnosticism, that He was but an inferior emanation or agent of the Supreme God.