Is 'amp' a technically invalid term? I've been told to use the term ampere in exams and class (I'm in high school), instead of amp as it's not a valid unit, although I've been using the amp for years along with all of my friends who do electronics.
Is this technically invalid or acceptable as far as the scientific consensus goes, and what would you think if you saw it used in a scientific paper?
 A: If I saw the word "amp" written as such in a paper in my field (astrophysics) it would strike me as a bit informal. I would expect to see the full "ampere" written.
That said, it is rare to actually write out the full name of a unit; usually it follows a number and is given its standard abbreviation. When abbreviated to e.g. "$5\ \mathrm{A}$", I would pronounce the quantity as "five amps" even when giving a formal presentation. I just wouldn't write "amp." (Similar to how I would use contractions while giving a formal presentation, but I wouldn't write them in a journal paper.)
Customs may vary from one field to another, however. Most scientific journals have very detailed style guides for authors that cover things like this. And even if you ignore their requests they often fix up such usages to standardize them before the article goes to print.
A: Technically, apparently, your teacher is correct.
BIPM and NIST
In the official brochure from the Bureau international des poids et mesures (BIPM, the keepers of SI units) in §5.1 Unit symbols we find:

It is not permissible to use abbreviations for unit symbols or unit names, such as sec
(for either s or second), sq. mm (for either mm2
or square millimetre), cc (for either
cm3
or cubic centimetre), or mps (for either m/s or metre per second). The use of the
correct symbols for SI units, and for units in general, as listed in earlier chapters of
this Brochure, is mandatory. In this way ambiguities and misunderstandings in the
values of quantities are avoided.

In NIST's official SI guide, §6.1.8 we find (thanks to Emilio):

6.1.8 Unacceptability of abbreviations for units
Because acceptable units generally have internationally recognized symbols and names, it is not permissible to use abbreviations for their unit symbols or names, such as sec (for either s or second), sq. mm (for either mm2 or square millimeter), cc (for either cm3 or cubic centimeter), mins (for either min or minutes), hrs (for either h or hours), lit (for either L or liter), amps (for either A or amperes), AMU (for either u or unified atomic mass unit), or mps (for either m/s or meter per second). Although the values of quantities are normally expressed using symbols for numbers and symbols for units (see Sec. 7.6), if for some reason the name of a unit is more appropriate than the unit symbol (see Sec. 7.6, note 3), the name of the unit should be spelled out in full.

Both sources agree that when printed, the unit's name should appear as the lowercase, non-italic: "ampere" and its symbol should be the uppercase roman script letter: $\mathrm{A}$.
When spoken, people regularly use "amp" as short for "ampere" (which never causes confusion), though it would appear, according to official recommendations, in printed material the full name should always be used.
IEEE
For engineers (specifically the IEEE) the policy seems more lax, though in an amusing way.
Specifically in IEEE Std. 260-1 [doi] we find in footnote 1:

The unit names ampere and second
have sometimes been abbreviated amp and sec, respectively, but this usage is now deprecated. The standard unit symbols for ampere
and second are A and s, respectively

But then in 2014 IEEE Standard's Style Manual [pdf], regarding footnotes in §16.2 Footnotes we find:

Mandatory requirements shall not be included in text footnotes because these footnotes are not
officially part of the standard.

so it would appear IEEE members are unbound from the deprecation mentioned.
A: According to the Wikipedia page, amp is acceptable, but is not a correct SI unit. I think your instructor is being thorough and making certain that you know the correct term to use.
A: Well, amp is also used as a short form of "amplifier". I highly suggest to use the full name of the unit or its symbol, i.e. Ampere or A. :)
A: For me in my own field (optics, where one most often comes across it in engineering considerations), "amps" is common spoken usage, particularly for compound words such as milliamp or microamp. 
For written usage, I'm afraid I like to see the full name - it is, after all, recalling a very great man of science André-Marie Ampère. Even so, curiously, the SI convention I believe is only to use the upper case "A" in the abbreviation, and the lower case for the full name (even thought it is someone's name); thus one writes "5 A" but "5 ampere" (note that one doesn't use the plural form in SI, either). 
If you think of "amp" as a kind of "diminutive" name, you won't go far wrong. My passport and other documents have my full forename in them, my friends simply call me "Rod"; likewise everyone calls my little son "Sascha" whereas his name on all documents is "Alexander".
