For me, tschoppi really nails the right response to this question.
Before you handle any chemical you are unfamiliar with, you should first read AND UNDERSTAND all facets of the MSDS (SDS) for that chemical. You need to understand the hazard potential, risk mitigation steps, emergency response strategies and disposal management of all chemicals you are handling.
If you have the capacity to legally obtain chemicals such as copper sulfate pentahydrate, you should also be able to obtain the MSDS (SDS). Google searching will also provide you with this information.
Now, with regards to $\ce{CuSO4.5H2O}$, it has a GHS signal word DANGER, with the following key safety statements:
Hazard Statements
- Toxic if swallowed.
- Causes skin irritation.
- Causes serious eye irritation.
- Very toxic to aquatic life.
Precautionary Statements
- Wash skin thoroughly after handling.
- Do not eat, drink or smoke when using this product.
- Avoid release to the environment.
- Wear protective gloves/ eye protection/ face protection.
Response Statements
- IF SWALLOWED: Immediately call a POISON CENTER or doctor/physician.
- IF ON SKIN: Wash with plenty of soap and water.
- IF IN EYES: Rinse cautiously with water for several minutes. Remove contact lenses, if present and easy to do. Continue rinsing.
- If skin irritation occurs: Get medical advice/ attention.
- If eye irritation persists: Get medical advice/ attention.
- Take off contaminated clothing and wash before reuse.
Additionally, it advises to wear correct respiratory protection (P2 or N99) and avoid breathing vapours mist or gas.
Given this information, it is unsurprising that you experienced an irritation-type reaction to breathing the vapours. So, how to avoid this next time? Read and understand the MSDS prior to use. Employ the correct protective equipment. Carry out the procedure in a suitably ventilated area, with active ventilation. This could be outside with a strong fan pushing vapours away.
If you are unsure about how to handle this chemical correctly, forgo the pretty colours on your rocket.