As you pointed out, though this may be basic biology, seeking clarification when receiving conflicting information is a good thing. Don't feel embarrassed for asking. :)
.. our molecular biology teacher told us that a double helix of DNA was composed of two DNA molecules linked together by hydrogen bonds.
Respectfully, your teacher is incorrect. A single, double-stranded DNA molecule is comprised of two helical shaped polynucleotides, and are connected together via hydrogen bonding.
Highlight of each polynucleotide
Highlight of hydrogen bonding
And just for further validation, according to Molecular Biology of the Cell, 4th ed., by Alberts B, Johnson A, Lewis J, et al.:
A DNA molecule consists of two long polynucleotide chains composed of four types of nucleotide subunits. Each of these chains is known as a DNA chain, or a DNA strand. Hydrogen bonds between the base portions of the nucleotides hold the two chains together.
So, it would seem that your teacher is referring to each polynucleotide, a.k.a. DNA strand, as a DNA molecule. Instead, she should use the verbiage: a single DNA molecule is composed of two DNA strands, which are helical-shaped polynucleotides.